Conceptual Profit Allocation Framework forConstruction Joint Ventures: Shapley Value Approach

Radwa Eissa1; Mohamed S. Eid, A.M.ASCE2; and Emad Elbeltagi, M.ASCE3

Abstract: Construction joint ventures (CJVs) execute business by pooling diverse technical and financial contributions from collaboratingentities. Traditional CJV profit-allocation approaches account only for investment shares, and do not address the marginal contribution ofthe participating parties. Therefore, disagreements may arise between stakeholders. This research aims to reduce profit-share-related disagree-ments among multiple CJV members by allocating profit based on the marginal contribution of each party. The authors developed a con-ceptual framework using the Shapley value as an alternative to the traditional investment-based approach. Three illustrative examplesdemonstrated the possible use of the developed conceptual framework. Results of the study highlighted the potential of Shapley valueas an alternative profit allocation scheme. The stability of the generated results was validated mathematically, and decision makers’ perceptionof fairness was addressed following the methods of prior experimental cooperative game theory research. This paper contributes to the bodyof knowledge by proposing an axiomatically fair methodology for profit-sharing negotiations among multiple collaborating parties in aproject. This approach can be utilized in other engineering domains where the management needs to foster stable and fair collaborationsamong its stakeholders. DOI: 10.1061/(ASCE)ME.1943-5479.0000911. © 2021 American Society of Civil Engineers.

Introduction

Strategic alliances are an essential instrument to withstand the soar-ing levels of complexity and competition in the construction marketin which globalization and integration of technology are changingthe way infrastructure projects are delivered. Construction jointventures (CJVs), a special form of strategic alliances, can be de-fined broadly as short-term contractual arrangements betweentwo or more firms in order to deliver engineering or constructionservices by jointly allocating technical and financial resources overthe duration of a single project (Ho et al. 2009; Viswanathan andJha 2020; Naylor and Lewis 2003).

Despite the collaborative benefits of CJVs and the emphasizedimportance of having a fair and comprehensive agreement, CJV-related disagreements are rather common (Frein 1980; Hong andChan 2014; Prasitsom and Likhitruangsilp 2015; Tetteh and Chan2019). Previous studies have stated that the selection of a CJVsponsor as well as the assignment of work packages and their as-sociated profit and risk shares are frequent causes of disagreement(Frein 1980; Munns et al. 2000; Norwood and Mansfield 1999;Prasitsom and Likhitruangsilp 2015; Shoubi et al. 2012; Tettehand Chan 2019). Such disagreements may cause one or more mem-bers to withdraw from the CJV, occasionally resulting in a haltingof the bidding process if the remaining members fail to secure

the bid independently (Frein 1980; Prasitsom and Likhitruangsilp2015). Moreover, even if a formation agreement has been estab-lished, subsequent disagreements about the sharing of profitand losses between CJV parties during the project may lead todisputes causing contract termination (Gunduz and Abdi 2020;Hwang et al. 2017; Mba and Agumba 2018a, b; Tetteh and Chan2019). Apportionment-related disagreements arise from the tradi-tional approach in sharing profit and losses based on the investmentratio, rather than accounting for the contribution and added valueto the CJV (Eissa et al. 2020; Hwang et al. 2017; Hsueh andYan 2011).

Hence, to minimize risks of a disagreement over CJV profitallocations, an alternative approach is needed to generate accept-able divisions that are perceived as fair to all collaborating entities.Because successful CJVs are a function of contributions from allparties involved, a fair CJV agreement should distribute coopera-tive gains in a manner that reflects these diverse contributions.Cooperative game theory (CGT) presents an ideal basis for profitallocations between CJV parties, owing to its marginal contribution-based solution concepts that generate axiomatically fair and efficientdivision sets for the benefit of cooperation (Estévez-Fernández2012). Various CGT solutions have been applied in constructionengineering and management research to generate fair and efficientallocations of cooperative benefits among construction coalitions(Asgari et al. 2014; Barough et al. 2012; Hafezalkotob et al. 2017)as well as stakeholders in integrated project delivery (IPD) teams(Teng et al. 2019). Accordingly, using a CGT solution, this paperaims to generate profit allocations based on the marginal contribu-tion of each party to the CJV, presenting an axiomatically fair alter-native to the traditional profit-sharing approaches.

Research Goal and Objectives

The goal of this research is to reduce disagreements over CJV profitshares. This paper presents a conceptual framework for alternativeprofit allocations based on the marginal contribution of eachparty rather than on investment- or scope-based approaches. Thedetailed objectives of the research were to (1) demonstrate the cost

1Research and Teaching Assistant, Dept. of Civil Engineering,Heliopolis Univ., Heliopolis, Cairo 11361, Egypt. ORCID: https://orcid.org/0000-0001-9923-6774. Email: radwa.yassin@hu.edu.eg

2Assistant Professor, Construction and Building Engineering, ArabAcademy for Science, Technology, and Maritime Transport, SheratonHeliopolis, Cairo 11799, Egypt (corresponding author). ORCID: https://orcid.org/0000-0002-5125-3986. Email: meid@aast.edu

3Professor, Dept. of Structural Engineering, Mansoura Univ., Mansoura35516, Egypt. ORCID: https://orcid.org/0000-0002-6568-3522. Email:eelbelta@mans.edu.eg

Note. This manuscript was submitted on July 31, 2020; approved onNovember 25, 2020; published online on March 5, 2021. Discussion periodopen until August 5, 2021; separate discussions must be submitted for in-dividual papers. This paper is part of the Journal of Management in En-gineering, © ASCE, ISSN 0742-597X.

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minimization potential of CJVs due to the pooling of technical andfinancial resources, (2) generate profit divisions among CJV partiesusing the Shapley value to account for the marginal contribution ofeach contractor, (3) assess the stability of the generated profit al-locations via (a) noncooperative game theory and (b) the propensityto disrupt of each party, and (4) compare the generated frameworkresults against profit allocations perceived as fair by impartial in-dustry practitioners.

Background Information

Construction Joint Ventures

A CJV typically refers to a contractual, nonincorporated entityenabling collaborating contractors to share financial and technicalresources over the duration of a single project (Ho et al. 2009;Viswanathan and Jha 2020; Naylor and Lewis 2003). In terms ofgovernance as well as reward and risk allocation mechanisms,CJVs are categorized into the following structures: (1) integratedCJVs, in which parties pool staff and resources to the CJV, and asingle team is established, sharing profit and losses proportional tothe equity invested by each party, and (2) nonintegrated CJVs, alsoreferred to as consortia, in which the project work packages aresplit among firms, and each party profits or incurs losses based ontheir performance of the assigned portions of the project (Chen andMessner 2009; Kale et al. 2013). According to Ho et al. (2009),the actual governance mechanism of a CJV lies within the intervalbetween both extremes of these structures.

Previous CJV research focused on the CJV formation motives(Chan et al. 2020; Girmscheid and Brockmann 2010; Gunduz andAbdi 2020; Kazaz and Ulubeyli 2009; Norwood and Mansfield1999), governance mechanisms (Han et al. 2019; Ho et al. 2009;Lin and Ho 2013; Xue et al. 2017), performance management andindicators (Mohamed 2003; Ozorhon et al. 2008, 2010, 2011) theassessment and management of risks (Bing et al. 1999; Hsueh et al.2007; Shen et al. 2001; Zhang and Zou 2007; Zhao et al. 2013), andthe critical success factors of CJVs (Adnan and Morledge 2003;Mba and Agumba 2018a, b). Studies highlighting CJV critical suc-cess factors emphasized the importance of having a comprehensiveand fair CJV agreement in order to avoid internal disagreementsamong CJV parties (Adnan et al. 2018; Mba and Agumba2018a, b; Han et al. 2019; Hong and Chan 2014). Furthermore, pre-vious research on the barriers and challenges to the formation of astable CJV stated that disagreements over the reward–risk sharingmethodology pose a critical risk on CJV stability (Bing et al. 1999;Chan et al. 2003; Gale and Luo 2004; Gunduz and Abdi 2020;Hwang et al. 2015, 2017; Lu et al. 2020; McIntosh and McCabe2003; Mikapagaro et al. 2018). Despite its emphasized importance,to the authors’ knowledge, the apportionment of profit in CJVagree-ments received very limited attention in the previous literature.

Previous research efforts on minimizing the risks of disagree-ments over profit allocations among collaborating parties domi-nantly featured two-firm profit allocation schemes in incorporatedjoint venture (JV) contexts (Darrough and Stoughton 1989; Duet al. 2006; Nakamura 2005; Lee and Yan 2019; Yan et al. 2006).Darrough and Stoughton (1989) studied the profit-sharing arrange-ments among two parties in a JVas a Bayesian bargaining game, inwhich each party has incomplete information about the other’s costs.Du et al. (2006) presented a negotiation-based profit-sharing schemeamong two JV parties, in which one party owns a new technologyand the other has better market knowledge, and both have and eachparty valuates the contribution of their counterpart independently.Nakamura (2005) and Lee and Yan (2019) analyzed the impact

of learning and technology transfer through the JV lifetime on eachparty’s bargaining power and, consequently, their ownership shares.However, the nature of the CJV formation agreement process isdissimilar to that in JVs in other industries (Girmscheid andBrockmann 2010). This is due to the difference in the JV structure,because contractual CJVs typically are formed on a project-basisand are relatively short-termed compared with incorporated JVs(Yan and Li 2011). Hence, findings from the JV literature in otherindustries cannot be transferred to CJVs without prior validation.

In the context of CJV profit sharing schemes, Yan et al. (2006)and Yan (2011) modeled the profit sharing process among two-partyCJVs as a sequential bargaining game, using fuzzy logic to quantifyeach party’s need for the project. This bargaining model wasadopted and modified by Yan and Li (2011) to account for the im-pact of the associated risks inherent with both parties on the out-come of the bargaining process. Another CJV profit-sharing schemewas presented by Hsueh and Yan (2011), which applied CGT as abasis for CJV partner evaluation and selection based on the gener-ated profit divisions for the international party in a two-firm CJV.

Thus, profit-sharing schemes addressed in the CJV literaturemostly focused on investment-based two-player bargaining games,and on one-sided decision support models. However, CJVs areformed to benefit from the collaboration between the participantsand capitalize on each party’s contribution. Therefore, there is aneed for a model that captures the contribution of each player inallocating the profits of a CJV. This research covers this knowledgegap by proposing a novel profit-sharing methodology among a num-ber of collaborating stakeholders in a CJV that accounts for the mar-ginal contribution of each party. This approach can be transformedto other alternative project delivery systems and different engineer-ing domains that require collaboration between stakeholders.

Cooperative Game Theory

Game theory is the study of situations of cooperation and conflictbetween rational decision makers, in which the actions and payoffsof each decision maker determine the overall outcome of the game(Ott 2006). Game theory was introduced in von Neumann andMorgenstern’s (1944), and has been applied in numerous fieldsof science since then (Eid et al. 2015).

Using quantitative models and hypothetical examples, gametheory provides insight into the strategic behavior of parties, seek-ing the maximization of their individual utility (Myerson 1991).The following elements are essential to describe a game: (1) players(the individuals taking part in the game), (2) a set of actions for eachplayer (options or moves), (3) players’ payoffs from each possiblecombination of actions, and (4) information available to players atdifferent stages in the game (Rasmusen 2006). The outcome of agame can be predicted using a combination of the best responsestrategies of each player (Madani 2010).

Interactions studied in game theory are classified into two mainbranches based on the relationship among players: (1) noncoopera-tive games, and (2) cooperative games. In noncooperative games,players do not have the incentive to cooperate, either due to a zero-sum game (in which gains for one player are losses for the other)or due to a lack of social ties such as trust, binding contracts, orcredible threats (Axelrod 1984). Thus, each player focuses only onmaximizing their own benefit, regardless of the total outcome ofthe game. Noncooperative games result in more realistic and stableoutcomes which might not necessarily be optimal (Madani 2010).This stable outcome is known as the Nash equilibrium, which is thecombined outcome of all players’ best responses, in which none ofthe players has an incentive to deviate from their adopted strategies(Gibbons 1992).

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On the other hand, cooperative games analyze interactionsamong collaborating entities, providing solution concepts that di-vide the generated benefit of cooperation on an axiomatic basis thatrepresents the notions of fairness and efficiency (de Clippel andRozen 2013). CGT has been beneficial to solving various resource-sharing problems, identifying (1) the possible coalitions that mayform, and (2) the fair divisions of the cooperative surplus amongcollaborating agents in a coalition (Hafezalkotob et al. 2017). Acooperative game typically includes the following: the grand coali-tion N, which contains all players; subset coalitions of N, denotedS; and a characteristic function v that defines a value νðSÞ whichrepresents the value created by members in subset coalition Swork-ing together. Similarly, the worth of the grand coalition νðNÞ isequal to the value created due to the collaboration of all players.CGT solution concepts generate division sets to distribute νðNÞamong coalition members (Moulin 2003).

Two of the most prominent CGT solution concepts are the coreand the Shapley value. The core solution concept, which was in-troduced by Gillies (1959), is motivated by the formation of stablecoalitions. The core solution concept generates a solution space ofefficient payoff distribution vectors that follow two rationality ax-ioms: (1) an individual rationality axiom (players receive at leasttheir own worth), and (2) a coalitional rationality axiom (a coalitionreceives no less than the sum of the earned values by its members)(Faigle et al. 2016). The main challenge to the core solution con-cept is that it is not unique; moreover, many games have no stableoutcomes, so the core does not exist for those games (Argoneto andRenna 2011; d’Eon et al. 2019).

Shapley (1953) introduced a cooperative game theoretic con-cept that generates a unique set of divisions for the benefit of co-operation known as the Shapley value. Shapley value–generatedpayoff allocations satisfy the following axioms: (1) efficiency,which means that all the surplus generated by the grand coalition(coalition of all players) has to be allocated; (2) symmetry, whichstates that two players making the same contribution to a coalitionshall receive equal payoffs; (3) a dummy player, which deals with aplayer making no contribution to any coalition by giving them nopayoffs; and (4) additivity, meaning that the sum of two coalitionalgames is equal to the sum of the awarded payoffs in both games(Myerson 1991). The Shapley value generates a unique distributionof joint benefits or costs—in the present case, the profits generatedby the CJV—that corresponds to a weighted average of the total ofincremental profits that a single party can add to any coalition itjoins. Unlike the core solution concept, the Shapley value alwaysexists for any cooperative game (d’Eon et al. 2019).

Various CGT solution concepts have been applied in the con-struction engineering and management literature on the allocationof cooperative costs or benefits among collaborating parties. One ofthe first applications of CGT in construction was introduced byPerng et al. (2005), who studied collaborating formwork subcon-tractors and the applied CGT solution concepts to assess the poten-tial cost savings due to the pooling of resources. Asgari et al. (2014)developed a model for subcontractor coalitions in a short-termpartnering case and generated profit allocations using four differentCGT solution concepts. Javanmardi et al. (2018) also studied sub-contractor coalitions, and developed a model using CGT for theallocation of collaborative benefits among subcontractors’ alliancesperforming high-reliability planning. Teng et al. (2019) presented aCGT model to allocate profits among collaborating stakeholders inIPD systems.

Framework Development

This section presents an overview of the conceptual profit allocationframework. First, the framework assumptions are listed to specifythe scope of the presented research, followed by a cost-minimizationmodule to estimate the potential costs of possible CJV coalitions.Finally, estimated CJV profits are allocated among collaboratingcontractors using the Shapley value.

Framework Assumptions

The proposed conceptual framework addresses CJV negotiationsamong three contractor firms, in which project work packages areassigned to the party that can perform at minimum cost. Accord-ingly, the marginal contribution of each firm is assumed to bethe cost savings brought by introducing the firm to the CJV. More-over, it is assumed that the negotiating qualified parties report theirtrue costs of the project work packages and that they already haveagreed on a contract price. Uncertainties associated with cost esti-mates are disregarded at this point, and will be addressed in futureresearch. It is assumed that the negotiating parties have agreed to theexclusivity of the bidding CJV (i.e., no party can bid with anotherCJV) in order to limit the outside options of each party. Finally, it isassumed that the bid award is based on the lowest price.

CJV Cost-Minimization Module

Before embarking on a project, involved stakeholders first performtheir market research and feasibility assessments in order to ensurethat establishing a CJV is the optimal form for project delivery(Walker and Johannes 2003). If a single contractor firm decidesto embark on a project independently, it can evaluate its expectedprofits by subtracting the total of its estimated costs for all projectactivities from the awarded contract amount

vðiÞ ¼�Vcontract −

Xnj¼1

Cij

�ð1Þ

where vðiÞ = profit generated by player i independently; Vcontract =agreed-upon contract price; Cij = cost for contractor i to performwork package j; and n = total number of project work packages.

On the other hand, in the case of a CJV, collaborating firms mustpreagree on the costs of their resources and assigned work packagesin order to determine their contract price and to form their CJVagreement for the project (Frein 1980).

When properly structured, CJVs are a favorable vehicle for proj-ect delivery due to their competitive advantage. This is highlightedin price competitiveness—because work packages are assigned toparties that can perform at minimum costs—and, consequently, in-crease profits for the collaborating parties. The total project costthrough the collaborative efforts of the joint venture is the sum ofall work packages when each work package j is assigned to con-tractor i who can perform it at minimum cost. This is calculated inEq. (2), where ArgMin searches for the minimum value C of workpackage j across all payers i in coalition S. Hence, the total profit forthe CJV can be obtained through subtracting the project cost fromthe agreed upon contract price [Eq. (3)]

CS ¼Xnj¼1

ArgMin½Cij;∀i ∈ S� ð2Þ

vðSÞ ¼ Vcontract − CS ð3Þ

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CJV Profit Allocation Module

After the expected profit of each subset CJV is calculated, theShapley value is used to generate marginal contribution-basedprofit divisions among the CJV members. The Shapley value pay-off division φ for player i belonging to S subset coalitions that canform a CJV is

φiðN;υÞ ¼X

S⊆Ni∈S

ðjSj− 1Þ!ðjNj− jSjÞ!jNj! · ½υðSÞ− υðS− figÞ� ð4Þ

where N = grand coalition that includes all possible CJV partici-pants; υðSÞ = value (profit) created by subset S CJV; and υðS −figÞ = value generated by subset coalition S without player i. Usingthe Shapley value, player i, receives a payoff distribution that isequal to a weighted average of i’s marginal contribution to all thesubset coalitions it can join. The marginal contribution of a player ito a subset coalition S is reflected in the added value earned by acoalition due to the presence of this player, ½υðSÞ − υðS − figÞ�.The weighted average is calculated by accounting for all the pos-sible subset coalitions that can be formed to include i.

Illustrative Case Studies

To illustrate the presented conceptual framework, three illustrativecase studies of hypothetical CJV projects among three parties, A,B, and C, were used. Contract amounts and project work packagesof Case studies 1 and 3 were adopted from actual constructionprojects (Arabtec 2019; SELI Overseas 2018), whereas Case study2 was adopted from the CJV literature (Hsueh and Yan 2011).Estimates of the cost of project work packages for each of thethree contractors in the presented case studies are provided to dem-onstrate the proposed profit-sharing methodology. The authors do

not have the actual cost of all work packages, but estimates wereobtained based on the work package descriptions as well as throughpublicly accessible information on the projects.

In all presented cases, there were seven possible coalitions S thatcould arise among the collaborating parties, three singletons (orsingle-party coalitions), three two-party CJVs, and a grand coali-tion of the three parties. These S coalitions are {A}, {B}, {C},{AB}, {AC}, {BC}, and {ABC}. The estimated cost and profitfor each CJV coalition were calculated using Eqs. (1)–(3).

The generated profit for each coalition was allocated amongcollaborating contractors using the Shapley value characteristicfunction via Eq. (4). The resulting profit allocations and their rel-ative percentages were calculated for all three cases. For compari-son purposes, investment-based allocations and percentages werecalculated as well. The following subsections elaborate the detailsof each illustrative case study project, including a brief projectdescription, work packages required, and background informationon the potential CJV parties and their associated project costs.

Case Study 1

In Case study 1, Contractor A, a large-scale construction firm,sought partners in order to bid for a residential complex construc-tion project; the estimated contract amount of the project was USD30,783,000. Both B and C were smaller-scale contractors that in-tended to join the project. Table 1 lists the project work packagesand the corresponding estimated costs of each contractor.

None of the three contractors could secure the project bid inde-pendently, because their individual costs were greater than the con-tract price. Although Firm A had the lowest total cost, it had onlythe minimum cost for Work package 1, whereas for the remainingsix work packages, Firms B and C could perform at lower cost.Table 2 lists the work packages (j) assigned to each firm underall possible CJV scenarios.

Table 1. Contractor cost estimates for Case study 1

Work package, j

Contractor cost estimates (USD)

A B C

1 Building construction and temporary site facilities 21,730,497 23,247,853 24,963,6242 Construction of MEP and infrastructure works 1,315,179 1,152,911 1,292,7083 Construction of roads 474,295 451,709 410,6454 Fence works and open spaces 4,713,222 4,807,407 4,325,1455 Landscape works 1,303,222 1,239,360 1,282,2436 Telecom 1,450,299 1,499,652 1,337,5917 Security network 13,257 12,275 13,134

Total cost 30,999,971 32,411,168 33,625,090

Total profit (contract price: USD 30,783,000) Losing bid Losing bid Losing bid

Table 2. CJV cost and profit estimates for Case study 1

Work package, j

CJV cost estimates (USD)

AB AC BC ABC

1 21,730,497 21,730,497 23,247,853 21,730,4972 1,152,911 1,292,708 1,152,911 1,152,9113 451,709 410,645 410,645 410,6454 4,713,222 4,325,145 4,325,145 4,325,1455 1,239,360 1,282,243 1,239,360 1,239,3606 1,450,299 1,337,591 1,337,591 1,337,5917 12,275 13,134 12,275 12,275

Total cost (USD) 30,750,273 30,391,963 31,725,780 30,208,424

Total profit (USD) 32,727 391,038 Losing bid 574,577

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Contractors B and C could not secure the bid even as a two-partyCJV, because their cost still surpassed the contract price (Table 2).Therefore A had the highest negotiation power in the coalition.However, the marginal contribution of Firms B and C should notbe neglected, owing to the increased profits due to their joiningCoalitions AC and AB respectively. Table 3 lists the calculatedShapley value–based profit allocations and their percentages com-pared with the investment-based allocations. Contactor A’s profitshare decreased from 71.94% through investment-based allocationto 46.85% using the Shapley value. This was due to accounting for

the other contractors’ contributions to the coalition, for which theyshould be properly and adequately rewarded, thus increasing theirshare from 7.96% and 20.1% to 12.74% and 40.41%, for Contrac-tors B and C, respectively.

Case Study 2

Case study 2 was a tunneling project with an estimated awardamount of USD 103,328,000, in which Contractor Awas a foreigntunneling firm, and B and C were local contractors, both potentialcandidates to partner with A. Detailed project data were adoptedfrom Hsueh and Yan (2011). Table 4 lists the project work packagesand the corresponding estimated costs of each contractor.

In this case, both A and C could secure the bid independently,because their cost was lower than the contract price. Owing to theexpertise of Firm A in tunneling, it could achieve the highest profitas a singleton. However, because Awas a foreign firm, it needed alocal counterpart (due to market entry legislations and accessibilityto local key resources). Table 5 lists the work packages assigned toeach firm under all possible CJV scenarios. Table 6 lists the calcu-lated Shapley value–based profit allocations and their percentagescompared with the investment-based allocations.

Accounting for the marginal contributions to the grand coalitioninstead of the investment shares resulted in a decrease in ContractorB’s profit share from 27.21% to 16.07%. This was because B as asingleton could not earn profit independently, unlike A and C. Inaddition, the added value created due to B joining both C and AC(to form BC and the grand coalition ABC, respectively) was min-imal. On the other hand, the contributions of A and C to the grandcoalition are evident in the surge in profit from BC to ABC (ac-counting for A’s contribution) and from AB to ABC (accounting forC’s contribution). Therefore, Shapley value divisions for the grandcoalition resulted in an increase in A’s share from 50.42% to 56.01%and of C’s share from 22.37% to 27.92%. However, investment-based divisions allocated a greater share to B than to Contractor C,even though C’s contribution to all the CJVs it can join was

Table 3. Profit allocations in Case study 1

Contractorfirm

Profit allocation to CJV parties (thousand USD)

Shapley value divisions Investment divisions

AB AC BC ABC AB AC BC ABC

A 16.36 195.52 — 269.19 29.20 280.02 — 413.3550.00% 50.00% — 46.85% 89.21% 71.61% — 71.94%

B 16.36 — — 73.20 3.53 — — 45.7450.00% — — 12.74% 10.79% — — 7.96%

C — 195.52 — 232.19 — 111.02 — 115.49— 50.00% — 40.41% — 28.39% — 20.10%

Table 6. Profit allocations in Case study 2

Contractorfirm

Profit allocation to CJV parties (million USD)

Shapley value divisions Investment divisions

AB AC BC ABC AB AC BC ABC

A 9.170 8.284 — 10.058 7.022 7.731 — 9.05363.27% 52.65% — 56.01% 48.45% 49.14% — 50.42%

B 5.323 — 1.112 2.886 7.471 — 1.240 4.88736.73% — 21.22% 16.07% 51.55% — 23.68% 27.21%

C — 7.450 4.126 5.013 — 8.003 3.997 4.017— 47.35% 78.78% 27.92% — 50.86% 76.32% 22.37%

Table 4. Contractor cost estimates for Case study 2

Work package, j

Contractor cost estimates (USD)

A B C

1 Civil works 25,120,000 22,561,920 19,097,9202 Tunneling works 43,040,960 57,712,960 55,760,6403 Indirect costs 31,319,360 23,232,000 25,455,040

Total costs (USD) 99,480,320 103,506,880 100,313,600

Expected profit (USD)(contract price: USD103,328,000)

3,847,680 Losing bid 3,014,400

Table 5. CJV cost and profit estimates for Case study 2

Work package, j

CJV cost estimates (USD)

AB AC BC ABC

1 22,561,920 19,097,920 19,097,920 19,097,9202 43,040,960 43,040,960 55,760,640 43,040,9603 23,232,000 25,455,040 23,232,000 23,232,000

Total cost (USD) 88,834,880 87,593,920 98,090,560 85,370,880

Total profit (USD) 14,493,120 15,734,080 5,237,440 17,957,120

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significantly higher. Hence, investment-based allocations may notbe acceptable to C, triggering a possible disagreement.

Case Study 3

In Case study 3, contractor firms A (tunneling expert), B (civilworks contractor), and C [mechanical, electrical, and plumbing(MEP) contractor] planned to collaborate in a CJV in order tobid for a large-scale infrastructure project. Project details, workpackages, and contract amount were adopted from an ongoingproject. The project data can be accessed at SELI Overseas (2018).The project includes the replacement of an outfall pipe of a waste-water treatment plant with a tunnel lined with precast segments.The project also includes installation of new pipes and valves aswell as plumbing, HVAC, and electrical works. Table 7 lists theproject work packages and the corresponding estimated costs ofeach contractor.

Similar to Case study 1, all three contractors could not securethe project independently. Furthermore, even though C had thesmallest scope/investment, it could provide significant cost savingsto the HVAC and MEP work package. Table 8 lists the work pack-ages assigned to each firm under all possible CJV scenarios.

Only AB and ABC were feasible CJV coalitions, because theirtotal costs were lower than the contract value (Table 8). However,

the difference between the profit earned in both CJV scenariosdemonstrates the significant contribution of Contractor C, eventhough its investment contribution was minimal. Accounting forContractor C’s marginal contribution resulted in an increase in itsprofit shares from 15.91% to 26.80%. Table 9 lists the calculatedShapley value–based profit allocations and their percentages com-pared with the investment-based allocations.

Solution Stability

Although the Shapley value generates axiomatically fair payoffdivisions, the satisfaction of CJV parties under such divisions needsto be evaluated. This is because the stability of a potential CJV isdependent on the extent to which each party accepts its assignedprofit allocations.

To assess the stability of the possible CJV coalitions, generatedprofit allocations need to be tested mathematically. Moreover,the stakeholders’ acceptance of such shares must be evaluated. Thefollowing subsections demonstrate the mathematical stability anda preliminary stakeholders’ evaluation of the generated outcomes.To provide theoretical soundness to the conceptual framework re-sults, two mathematical evaluations were performed: (1) the prob-lem at hand was transformed into a noncooperative game andsolved for the Nash equilibrium, and (2) the propensity to disrupt(PTD) ratio of each party was calculated. Moreover, questionnaireswere utilized to provide adequate insight into the actual preferencesand behavior of decision makers.

Noncooperative Game and Nash Equilibrium

To evaluate the stability of the possible CJVs outcomes under bothprofit-allocation scenarios, the studied game was solved from anoncooperative viewpoint. This was done by transforming the gen-erated profit allocations into payoffs of a noncooperative strategic-form game and solving for the Nash equilibrium (NE). AlthoughNE is a noncooperative concept, it can be utilized to test the sta-bility of the outcomes of a cooperative game (Stolwijk 2010). Eissaet al. (2020) thoroughly discussed transforming the CJV character-istic function game into a noncooperative strategic-form game andsolving for Nash equilibrium. Unlike the cooperative games dis-cussed in the previous sections, players in a noncooperative gameadopt their strategies based on self-interest, aiming to maximizetheir individual utility regardless of the total outcome of the game.A strategy profile—which is a set that assigns a strategy to beadopted by each player—is a NE if none of the players would in-crease their utility by unilaterally deviating from their adopted strat-egy (Matsumoto and Szidarovszky 2016). In the presented casestudies, each of the three players had three strategies: (1) indepen-dent contracting, (2) join only one of the other two firms in a two-party CJV, or (3) join the grand CJV coalition in a three-party CJV.Accordingly, the game had 64 possible outcomes reflecting all thepossible combinations of the three player strategies. For the playersto obtain their corresponding profit payoff allocations, their CJVpreferences had to match; otherwise, no agreement was formed andplayers received their independent contracting payoffs. Tables 10and 11 list the noncooperative strategic-form game payoff matrixesfor the first case study under Shapley value–based and investment-based profit allocations, respectively. Games were solved for the NEusing Gambit version 16.0.1, a software package for solving non-cooperative game-theoretic models. Resulting NE strategies andoutcomes are highlighted in bold in Tables 10 and 11.

The results of the presented games demonstrated that thethree-party CJV was the stable NE outcome under both Shapleyvalue–based and investment-based allocations. This also was the

Table 9. Profit allocations in Case study 3

Contractorfirm

Profit allocation to CJV parties (million USD)

Shapley value divisions Investment divisions

AB AC BC ABC AB AC BC ABC

A 1.160 — — 4.327 0.971 — — 5.21650.00% — — 36.60% 41.87% — — 44.13%

B 1.160 — — 4.327 1.349 — — 4.72350.00% — — 36.60% 58.13% — — 39.96%

C — — — 3.167 — — — 1.881— — — 26.80% — — — 15.91%

Table 7. Contractor cost estimates for Case study 3

Work package, j

Cost estimates of each firm (USD)

A B C

1 Tunneling works 77,650,000 120,500,000 Out of scope2 Civil works 92,345,500 70,310,000 Out of scope3 HVAC and MEP works 40,000,000 37,500,000 28,000,000

Total costs (USD) 209,995,500 228,310,000 N/A

Expected profit (USD)(contract amount:USD 187,780,000)

Losing bid Losing bid Losing bid

Table 8. CJV cost and profit estimates for Case study 3

Work package, j

CJV cost estimates (USD)

AB AC BC ABC

1 77,650,000 77,650,000 120,500,000 77,650,0002 70,310,000 92,345,500 70,310,000 70,310,0003 37,500,000 28,000,000 28,000,000 28,000,000

Total cost (USD) 185,460,000 197,995,500 218,810,000 175,960,000

Total profit (USD) 2,320,000 Losing bid Losing bid 11,820,000

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equilibrium outcome for the other two case studies. This was be-cause all parties would earn more by collaborating under both di-vision schemes, and none had an incentive to deviate from the grandcoalition if the other two parties remained in. Accordingly, it can beassumed that both profit-allocation scenarios were equally stablefrom a noncooperative perspective, generating the same CJV forma-tion. Nevertheless, the negotiation power of each player and hencethe stability of the CJV formation need to be tested. The followingsubsection presents the calculation of the PTD of each party thatevaluates the negotiation power of each participant under both al-location schemes.

Propensity to Disrupt

The PTD was introduced by Gately (1974) and was utilized inthe multiple cooperative game theory literature to evaluate thestability of coalitions (Asgari et al. 2014). For a coalition N ¼f1; 2; : : : ; ng, if player i withdraws from the coalition, it may

result in a loss (or profit) for the remaining parties. Let x ¼ðx1; x2; : : : ; xnÞ represents the original payoff allocations for thecoalition (for example, Shapley value–based or investment-basedprofit allocations). Then, if player i breaks away from the coalition,the player incurs a loss of xi–υðfigÞ. The losses incurred by theremaining parties in the coalition can be defined as

Pj≠i½xj −

υðN \ figÞ� (Littlechild and Vaidya 1976).Accordingly, the PTD or the disruption due to the withdrawal

of player i from coalitionN can be evaluated as the ratio of what theplayers in coalition N lose to what player i itself loses if it breaksaway. Hence, the PTD for any player i in a coalition N can be cal-culated using (Straffin 1993)

PTDiðxÞ ¼P

j≠i½xðjÞ − vðN \ figÞ�½xðiÞ − vðfigÞ� ð5Þ

A high PTD for player i provides them with a stronger negationpower, thus creating instability in the coalition. Accordingly, the

Table 10. Case study 1 payoff matrix—Shapley value allocations (thousand USD)

Firm A Firm C

Firm B

B AB BC ABC

A C (0,0,0) (0,0,0) (0,0,0) (0,0,0)AC (0,0,0) (0,0,0) (0,0,0) (0,0,0)BC (0,0,0) (0,0,0) (0,0,0) (0,0,0)ABC (0,0,0) (0,0,0) (0,0,0) (0,0,0)

AB C (0,0,0) (16.36,16.36,0) (0,0,0) (0,0,0)AC (0,0,0) (16.36,16.36,0) (0,0,0) (0,0,0)BC (0,0,0) (16.36,16.36,0) (0,0,0) (0,0,0)ABC (0,0,0) (16.36,16.36,0) (0,0,0) (0,0,0)

AC C (0,0,0) (0,0,0) (0,0,0) (0,0,0)AC (195.52,0,195.52) (195.52,0,195.52) (195.52,0,195.52) (195.52,0,195.52)BC (0,0,0) (0,0,0) (0,0,0) (0,0,0)ABC (0,0,0) (0,0,0) (0,0,0) (0,0,0)

ABC C (0,0,0) (0,0,0) (0,0,0) (0,0,0)AC (0,0,0) (0,0,0) (0,0,0) (0,0,0)BC (0,0,0) (0,0,0) (0,0,0) (0,0,0)ABC (0,0,0) (0,0,0) (0,0,0) (269.19,73.2,232.19)

Table 11. Case study 1 payoff matrix—investment-based allocations (thousand USD)

Firm A Firm C

Firm B

B AB BC ABC

A C (0,0,0) (0,0,0) (0,0,0) (0,0,0)AC (0,0,0) (0,0,0) (0,0,0) (0,0,0)BC (0,0,0) (0,0,0) (0,0,0) (0,0,0)ABC (0,0,0) (0,0,0) (0,0,0) (0,0,0)

AB C (0,0,0) (29.20,3.53,0) (0,0,0) (0,0,0)AC (0,0,0) (29.20,3.53,0) (0,0,0) (0,0,0)BC (0,0,0) (29.20,3.53,0) (0,0,0) (0,0,0)ABC (0,0,0) (29.20,3.53,0) (0,0,0) (0,0,0)

AC C (0,0,0) (0,0,0) (0,0,0) (0,0,0)AC (280.02,0,111.02) (280.02,0,111.02) (280.02,0,111.02) (280.02,0,111.02)BC (0,0,0) (0,0,0) (0,0,0) (0,0,0)ABC (0,0,0) (0,0,0) (0,0,0) (0,0,0)

ABC C (0,0,0) (0,0,0) (0,0,0) (0,0,0)AC (0,0,0) (0,0,0) (0,0,0) (0,0,0)BC (0,0,0) (0,0,0) (0,0,0) (0,0,0)ABC (0,0,0) (0,0,0) (0,0,0) (413.35,45.74,115.49)

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lower the PTD for all players, the more stable is the coalition.A player with a PTD of zero would have no desire to leave thecoalition. Furthermore, a negative PTD is an expression of hyper-enthusiasm for cooperation (Gately 1974).

Fig. 1 shows the calculated PTD ratios for all players in thegrand coalition (three-party CJV) for the three illustrative examplesunder the Shapley value–based versus investment-based allocations.The maximum PTD values were associated with investment-basedallocations in all three cases. Thus, the players had a higher prob-ability of abandoning the collation due to investment-based profitnegotiations. On the other hand, Shapley value–based divisionshad relatively lower values. In addition, the variances among thePTD values for each party using Shapley value allocations were rel-atively nominal compared with those yielded by investment-baseddivisions. In other words, Shapley value–generated divisions ren-dered the interests as well as negotiation powers of all parties almostthe same. This mathematically supports the fairness of the profitshares provided using the Shapley value, which outperforms theconventional investment-based approach in terms of PTD ratiosfor the presented case studies.

Fairness: Shapley Value Axioms versusIndustry Perceptions

The previous section evaluated the fairness and stability of gener-ated payoff allocations based on mathematical grounds. However,the fairness axioms behind the Shapley value may not always fullycapture the human perception of fairness (d’Eon et al. 2019). Pre-vious experimental work investigating human agents’ fair rewarddivisions for the surplus of cooperation indicated that human-baseddivisions are convex combinations of the Shapley value and equaldivisions (de Clippel and Rozen 2013). Adapting de Clippel andRozen’s (2013) methodology to a larger set of games, d’Eon andLarson (2020) concluded that human-based divisions did not al-ways align with the Shapley value, but were proportional to thevalues of single-player coalitions.

Because the negotiations prior to CJV formation are dependenton human decision-making, it is necessary to compare the gener-ated profit allocations in the presented conceptual framework basedon fairness axioms to what is perceived as fair divisions from thepoint of view of construction stakeholders. Fourteen constructionindustry practitioners were presented with the three illustrative casestudies and were asked to allocate profit percentages to each firmfrom their point of view as impartial decision makers. Participantsalso were asked to justify their assigned allocations.

In terms of geographical location, 10 participants were locatedin Egypt, 2 were located in Canada, 1 was located in the UnitedKingdom, and 1 was located in South Africa. Fig. 2 lists the years

of experience of participants in the construction industry, all ofwhom had taken part in at least one CJV project. The average num-ber of CJV projects per participant was 3.64. The lack of geographi-cal diversity in addition to the limited number of participants and theaverage number of projects per participant are considered as limi-tations of this research. Therefore, the results obtained from thisquestionnaire were used as a preliminary assessment of the concep-tual framework.

Profit percentages assigned by the participants for the three casesare given in Fig. 3 using ternary plots. Respondents’ allocationsare plotted as shaded circles, and darker areas represent overlappingallocations. Fig. 3 also shows the Shapley value and investmentratio-based divisions as well as the averaged allocations of therespondents for Players A, B, and C. Furthermore, the averageamounts allocated to each firm, based on the inputs of the 14construction industry participants, and the Shapley value– andinvestment-based allocations in all the three cases are plotted inFig. 4. The absolute differences among both division schemes andthe respondents’ average allocations are listed in Table 12.

Due to the limited number of responses, results of the perceptionof fairness questionnaire could not be deemed conclusive. However,results of the collected questionnaires shed light on the potential ofShapley value as an alternative profit allocation approach. This canbe observed in the resulting average respondents’ allocations inTable 12, which demonstrate that six of the nine average allocationsprovided were closer to the Shapley value divisions than to theinvestment-based allocations. Furthermore, another six of the ninerespondents’ average allocations fell in the intervals between bothprofit allocation schemes (Fig. 4). However, further data collectionand analyses are needed to conclusively validate decision makers’perceived sense of fairness of the presented conceptual frameworkresults.

Discussion and Recommendations for Future Work

Results of the proposed conceptual framework demonstrated thatthe Shapley value potentially can be an alternative CJV profit

Investment Investment Investment

3 esaC2 esaC1 esaCA 1.134 0.39 0.428 0.704 1.731 1.266B 1.494 2.993 -0.229 -0.545 1.731 1.502C 1.155 3.333 -0.775 -0.551 2 4.05

-2

0

2

4

6

PT

DShapley

valueShapley

valueShapley

value

Fig. 1. PTD ratios for the grand coalitions in the three case studies.

0

2

4

6

8

< 5 Years 5 - 10 Years > 10 Years

Nu

mb

er o

f P

arti

cip

ants

Years of Experience

Fig. 2. Participant years of experience in the construction industry.

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allocation scheme to the traditional investment-based approach.The proposed Shapley value profit allocation scheme takes into ac-count the marginal contribution of each party belonging to the co-alition, providing axiomatically fair and stable divisions that satisfythe rationality constraint for each player—i.e., none of the contrac-tors receives an allocation lower than their profit under individualoperations. The suggested framework accounts for the marginalcontribution of each party as the estimated cost savings that a partybrings to the CJV. Thus, players with small investment but highoverall cost reduction are adequately rewarded, as demonstratedfor Contractor C in Case study 3. Likewise, if a player(s) doesnot have a significant contribution—either independently or to theCJVs it joins—they will be rewarded accordingly. This was ob-served in Case study 1, in which Contractor B had minimal impact

on coalition AB and no positive impact on BC, and thus had thelowest share in the grand coalition.

Solving the CJV profit-allocation game from a noncooperativeperspective yielded the same NE strategies under both Shapleyvalue–based and investment-based profit allocation scenarios. How-ever, the Shapley value generated more-stable outcomes in terms ofthe PTD ratio. Therefore, mathematically, Shapley value profit al-location outperformed the traditional investment-based approach.

0.00%

20.00%

40.00%

60.00%

80.00%

A B C A B C A B C

Case 1 Case 2 Case 3

Pro

fit

Allo

cati

on

%

Players in each Case Study

Shapley value

Investment-Ratio

Respondents Average

Fig. 4. Respondents’ average allocations versus both divisions.

Table 12. Participants’ average allocations

Casestudy Firm

Profit allocation

Absolute differencefrom respondents’

average

Shapleyvalue (%)

Investment-based (%)

Respondents’average (%)

Shapleyvalue (%)

Investment-based (%)

1 A 46.85 71.94 55.87 9.02 16.07B 12.74 7.96 21.30 8.56 13.34C 40.41 20.10 22.83 17.58 2.73

2 A 56.01 50.42 48.98 7.03 1.44B 16.07 27.21 25.76 9.69 1.45C 27.92 22.37 25.19 2.73 2.82

3 A 36.60 44.13 39.61 3.01 4.52B 36.60 39.96 35.45 1.15 4.51C 26.79 15.91 24.95 1.84 9.04

Fig. 3. Participant allocations for the three illustrative cases.

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Nonetheless, the industry representatives in the questionnaire didnot conclusively agree with such shares. The experiment showedthat 6 of the 9 (3 players in 3 case studies) average allocationsprovided by 14 impartial industry practitioners fell in the intervalsbetween the Shapley value–based and investment-based divisions(Fig. 4). This result sheds light on the potential of the proposedconceptual framework to be adopted by decision makers. However,the results do not show total approval or disapproval of the Shapleyvalue.

In the collected questionnaire, some of the participants justifiedtheir generated divisions by accounting for the risks includedwithin each package—for example, tunneling work packages areriskier than MEP work packages, and therefore the party executingthe tunneling works should be entitled to more profit. This clearlyhighlights the unsuitability of the investment-based shares in CJVs,because it fails to account for uncertainties. Although cost savingscan provide a simplified representation of the marginal contributionapproach, quantifying other contribution factors such as risk reduc-tion, market knowledge and access key to local resources, andso forth might provide enhanced results. Addressing such factorswill meet industry needs, and more decision makers would agree onthe results. Future research thus is required to account for thosefactors in addition to investigating the decision makers’ preferencesregarding the Shapley value divisions. Such research needs to in-corporate a statistically significant sample of respondents as well asin-person interviews and focus groups.

Another factor that poses a challenge for this conceptual frame-work is the accuracy of the cost estimates reported by each party.Similar to construction bidding, reported estimates can be suscep-tible to various sources of inaccuracy. For example, inaccuraciesmay occur due to the fact that contractors cannot know the exactvalue of their costs for the project at such an early phase (Akinciand Fischer 1998; Chen et al. 2019; Hoseini et al. 2020; Hashemiet al. 2020). Accurate cost reporting incentivization and governancemechanisms may be beneficial for this approach in order to gen-erate more-valid allocations (Liu et al. 2019; Yao et al. 2020).Therefore, future extensions of the conceptual framework shouldaddress the impact of cost-estimate inaccuracies and determinewhether it yields the predicted results.

Simplifications of the CJV negotiation process were made in or-der to demonstrate the concept and provide an approachable meth-odology. This was done by estimating the CJV gains attributed toeach party based on their reported work package cost estimates inthe illustrative case studies. However, technically, such an approachmight require multiple rounds of negotiation and cross-validation toproperly estimate the work packages in order to evaluate the con-tribution of each party. Therefore, future work is needed to fill thegap between the theoretical work package allocation approach andthe construction industry practices.

Another extension of the research is to investigate the potentialof integrating this marginal contribution-based approach intoexisting traditional CJV standard agreements and project contracts.This investigation should provide solutions and insights into furthercontract amendments needed to accommodate such a transitionfrom investment to contribution-based profit shares.

Conclusions

This paper presents a conceptual framework that assists in deter-mining the maximum attainable profit by potential CJV coalitionsof multiple contractors, in addition to providing a stable and fairalternative profit-allocation scheme based on marginal contribu-tion. Accounting for such contributions is crucial in order to reach

a fair agreement, particularly in CJVs among firms with differentareas of specialty. The Shapley value was applied as a profit-sharingscheme for CJV negotiations to reduce disagreements that mightarise due to traditional allocations based on the investment ratio ofeach party, hence assisting stakeholders to define their fair sharesof profit, enhancing CJV formation negotiations, and potentiallyreducing the risk of disagreements.

Multiple case studies served as simplified illustrative numericalexamples to demonstrate the proposed solution in CJVs amongthree contractors. The presented framework can be generalized toaccount for more contractors to reflect a more realistic image of themarket and to identify coalitions that are most likely to form basedon their synergistic properties.

The stability of the generated results was validated math-ematically via noncooperative games and by calculating the pro-pensity to disrupt ratio for each player. This demonstrated lowermaximum disruption ratios compared with the traditional ap-proach. In addition, the gap between axiomatic sense of fairnessand human opinions (industry practitioners) was addressed via aquestionnaire.

For future work, possible enhancements to the proposed con-ceptual framework can provide more-accurate solutions to theprofit allocation problem in CJVs. The uncertainty associatedwith the reported cost estimates should be taken into considera-tion, because it may impact the generated allocations. Althoughestimated cost savings can denote a simplified representationof the marginal contribution, quantifying other contributionssuch as risk reduction, market knowledge and accessibility to keylocal resources, and so forth can enhance the generated results.Moreover, in-depth interviews with industry experts can providea clearer understanding of the industry perceptions regardingCJV profit allocations, and identify potential solutions for thechallenges of the framework, enhancing the acceptability of thegenerated allocations.

Another direction for future work is accounting for alternativeoutside options for the collaborating parties, i.e., joining other CJVcoalitions. This can be done by generalizing the model to include alarger number of contractors; consequently, the grand coalition willnot always be the most efficient solution, and subset CJVs may bemore feasible. In addition, investigating the potential implicationsof integrating the presented approach into standard CJVagreementsand contract forms can identify possible amendments for such stan-dard forms.

The presented conceptual framework contributes to the bodyof knowledge by providing a mathematical approach that fosterscollaboration between different stakeholders based on fair agree-ments. The proposed conceptual framework will contribute tothe industry by defining stable CJV agreements that account forstakeholders’ marginal contributions and reduce disagreementsbetween participating entities of a CJV. The application of theframework can be extended to agreements among other collabo-rating stakeholders, for example in design–build JVs or amongstakeholders in projects adopting alternative delivery systems.Ultimately, this novel approach can be incorporated in variousengineering domains that require stable collaboration betweenits stakeholders.

Data Availability Statement

Some or all data, models, or code that support the findings of thisstudy are available from the corresponding author upon reasonablerequest.

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References

Adnan, H., and R. Morledge. 2003. “Joint venture projects in Malaysianconstruction industry factors critical to success.” In Vol. 2 of Proc., 19thAnnual ARCOM Conf., 765–774. Portsmouth, UK: Association ofResearchers in Construction Management.

Adnan, H., M. R. Rosman, Z. Z. Ahmad Rashid, N. Mohamad Yusuwan,and N. A. Bakhary. 2018. “Application of Delphi expert panel in jointventure projects in Malaysian construction industry.” In Vol. 117 ofProc., IOP Conf. Series: Earth and Environmental Science. Bristol,UK: IOP Publishing.

Akinci, B., and M. Fischer. 1998. “Factors affecting contractors’ risk of costoverburden.” J. Manage. Eng. 14 (1): 67–76. https://doi.org/10.1061/(ASCE)0742-597X(1998)14:1(67).

Arabtec. 2019. “Arabtec awarded AED 298 million contract in uptownCairo development by Emaar Misr.” Accessed November 30, 2019.https://www.arabtecuae.com/news-media/news-highlights/arabtec-awarded-aed-298-million-contract-in-uptown-cairo-development-by-emaar-misr/.

Argoneto, P., and P. Renna. 2011. Innovative tools for business coalitions inB2B applications: How negotiation, auction and game theory can sup-port small- and medium-sized business in E-business. London: Springer.

Asgari, S., A. Afshar, and K. Madani. 2014. “Cooperative game theoreticframework for joint resource management in construction.” J. Constr.Eng. Manage. 140 (3): 04013066. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000818.

Axelrod, R. 1984. The evolution of cooperation. New York: Basic Books.Barough, A. S., M. V. Shoubi, and M. J. E. Skardi. 2012. “Application of

game theory approach in solving the construction project conflicts.”Procedia—Soc. Behav. Sci. 58 (Oct): 1586–1593. https://doi.org/10.1016/j.sbspro.2012.09.1145.

Bing, L., R. L.-K. Tiong, W. W. Fan, and D. A.-S. Chew. 1999. “Risk man-agement in international construction joint ventures.” J. Constr. Eng.Manage. 125 (4): 277–284. https://doi.org/10.1061/(ASCE)0733-9364(1999)125:4(277).

Chan, A. P. C., D. W. M. Chan, and K. S. K. Ho. 2003. “Partnering inconstruction: Critical study of problems for implementation.” J. Man-age. Eng. 19 (3): 126–135. https://doi.org/10.1061/(ASCE)0742-597X(2003)19:3(126).

Chan, A. P. C., M. O. Tetteh, and G. Nani. 2020. “Drivers for internationalconstruction joint ventures adoption: A systematic literature review.”Int. J. Constr. Manage. 1–13. https://doi.org/10.1080/15623599.2020.1734417.

Chen, C., and J. I. Messner. 2009. “Entry mode taxonomy for internationalconstruction markets.” J. Manage. Eng. 25 (1): 3–11. https://doi.org/10.1061/(ASCE)0742-597X(2009)25:1(3).

Chen, Y., Z. Hu, and Q. Liu. 2019. “Exploring the properties of costoverrun risk propagation network (CORPN) for promoting cost man-agement.” J. Civ. Eng. Manage. 25 (1): 1–18. https://doi.org/10.3846/jcem.2019.7462.

Darrough, M. N., and N. M. Stoughton. 1989. “A bargaining approach toprofit sharing in joint ventures.” J. Bus. 62 (2): 237–270. https://doi.org/10.1086/296461.

de Clippel, G., and K. Rozen. 2013. Fairness through the lens of co-operative game theory: An experimental approach. Cowles FoundationDiscussion Papers 1925. New Haven, CT: Cowles Foundation for Re-search in Economics.

d’Eon, G., J. Goh, K. Larson, and E. Law. 2019. “Paying crowd workersfor collaborative work.” In Proc., ACM on Human-Computer Interac-tion, 24. New York: Association for Computing Machinery.

d’Eon, G., and K. Larson. 2020. “Testing axioms against human rewarddivisions in cooperative games.” In Proc., 19th Int. Conf. AutonomousAgents and Multiagent Systems (AAMAS 2020), 312–320. Richland,SC: International Foundation for Autonomous Agents and MultiagentSystems.

Du, L., Q. Hu, and L. Liu. 2006. “A profit sharing scheme for a two-firmjoint venture.” Eur. J. Oper. Res. 170 (1): 277–292. https://doi.org/10.1016/j.ejor.2004.06.025.

Eid, M. S., I. H. El-adaway, and K. T. Coatney. 2015. “Evolutionary stablestrategy for postdisaster insurance: Game theory approach.” J. Manage.

Eng. 31 (6): 04015005. https://doi.org/10.1061/(asce)me.1943-5479.0000357.

Eissa, R., M. S. Eid, and E. Elbeltagi. 2020. “A cooperative game theoreticmodel for revenue sharing in construction joint ventures.” In Proc.,Construction Research Congress 2020, 1149–1157. Reston, VA:ASCE. https://doi.org/10.1061/9780784482889.122.

Estévez-Fernández, A. 2012. “A game theoretical approach to sharing pen-alties and rewards in projects.” Eur. J. Oper. Res. 216 (3): 647–657.https://doi.org/10.1016/j.ejor.2011.08.015.

Faigle, U., M. Grabisch, A. Jiménez-Losada, and M. Ordonez. 2016.“Games on concept lattices: Shapley value and core.” Discrete Appl.Math. 198 (Jan): 29–47. https://doi.org/10.1016/j.dam.2015.08.004.

Frein, J. 1980. Handbook of construction management and organization.New York: Springer.

Gale, A., and J. Luo. 2004. “Factors affecting construction joint venturesin China.” Int. J. Project Manage. 22 (1): 33–42. https://doi.org/10.1016/S0263-7863(03)00012-7.

Gately, D. 1974. “Sharing the gains from regional cooperation: A gametheoretic application to planning investment in electric power.” Int.Econ. Rev. 15 (1): 195–208. https://doi.org/10.2307/2526099.

Gibbons, R. 1992. Game theory for applied economists. Princeton, NJ:Princeton University Press.

Gillies, D. B. 1959. “3. Solutions to general non-zero-sum games.” In Vol.IVof Contributions to the theory of games, edited by A. W. Tucker andR. D. Luce, 47–86. Princeton, NJ: Princeton University Press.

Girmscheid, G., and C. Brockmann. 2010. “Inter- and intraorganizationaltrust in international construction joint ventures.” J. Constr. Eng. Man-age. 136 (3): 353–360. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000142.

Gunduz, M., and E. A. Abdi. 2020. “Motivational factors and challengesof cooperative partnerships between contractors in the constructionindustry.” J. Manage. Eng. 36 (4): 04020018. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000773.

Hafezalkotob, A., E. Hosseinpour, M. Moradi, and K. Khalili-Damghani.2017. “Multi-resource trade-off problem of the project contractors ina cooperative environment: Highway construction case study.” Int. J.Manage. Sci. Eng. Manage. 13 (2): 129–138. https://doi.org/10.1080/17509653.2017.1323240.

Han, L., S. Zhang, P. Ma, and Y. Gao. 2019. “Management control ininternational joint ventures in the infrastructure sector.” J. Manage.Eng. 35 (1): 04018051. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000665.

Hashemi, S. T., O. M. Ebadati, and H. Kaur. 2020. “Cost estimation andprediction in construction projects: A systematic review on machinelearning techniques.” SN Appl. Sci. 2 (10): 1703. https://doi.org/10.1007/s42452-020-03497-1.

Ho, S. P., Y.-H. Lin, W. Chu, and H.-L. Wu. 2009. “Model for organiza-tional governance structure choices in construction joint ventures.”J. Constr. Eng. Manage. 135 (6): 518–530. https://doi.org/10.1061/(ASCE)0733-9364(2009)135:6(518).

Hong, Y., and D. W. M. Chan. 2014. “Research trend of joint venturesin construction: A two-decade taxonomic review.” J. Facil. Manage.12 (2): 118–141. https://doi.org/10.1108/JFM-04-2013-0022.

Hoseini, E., P. van Veen, M. Bosch-Rekveldt, and M. Hertogh. 2020. “Costperformance and cost contingency during project execution: Comparingclient and contractor perspectives.” J. Manage. Eng. 36 (4): 05020006.https://doi.org/10.1061/(ASCE)ME.1943-5479.0000772.

Hsueh, S.-L., Y.-H. Perng, M.-R. Yan, and J.-R. Lee. 2007. “On-line multi-criterion risk assessment model for construction joint ventures in China.”Autom. Constr. 16 (5): 607–619. https://doi.org/10.1016/j.autcon.2007.01.001.

Hsueh, S.-L., and M.-R. Yan. 2011. “Contribution-based profit sharingscheme for joint ventures.” Technol. Econ. Dev. Econ. 17 (3): 445–458.https://doi.org/10.3846/20294913.2011.580578.

Hwang, B.-G., X. Zhao, and E. W. Y. Chin. 2017. “International construc-tion joint ventures between Singapore and developing countries: Riskassessment and allocation preferences.” Eng. Constr. Archit. Manage.24 (2): 209–228. https://doi.org/10.1108/ECAM-03-2015-0035.

Hwang, B.-G., X. Zhao, and G. S. Yu. 2015. “Risk identification andallocation in underground rail construction joint ventures: Contractors’

© ASCE 04021016-11 J. Manage. Eng.

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nloa

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asc

elib

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.org

by

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b A

cade

my

For

Scie

nce

& T

ech

on 0

3/08

/21.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

perspective.” J. Civ. Eng. Manage. 22 (6): 758–767. https://doi.org/10.3846/13923730.2014.914095.

Javanmardi, A., S. A. Abbasian-Hosseini, M. Liu, and S. M. Hsiang. 2018.“Benefit of cooperation among subcontractors in performing high-reliable planning.” J. Manage. Eng. 34 (2): 04017062. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000578.

Kale, V. V., S. S. Patil, A. R. Hiravennavar, and S. K. Kamane. 2013. “Jointventure in construction industry.” IOSR J. Mech. Civ. Eng. 3 (1): 60–65.

Kazaz, A., and S. Ulubeyli. 2009. “Strategic management practices inTurkish construction firms.” J. Manage. Eng. 25 (4): 185–194. https://doi.org/10.1061/(ASCE)0742-597X(2009)25:4(185).

Lee, Y.-H., and M.-R. Yan. 2019. “Factors influencing agents’ bargainingpower and collaborative innovation.” Asia Pac. J. Marketing Logist.31 (2): 559–574. https://doi.org/10.1108/APJML-09-2017-0217.

Lin, Y.-H., and S. P. Ho. 2013. “Impacts of governance structure strategieson the performance of construction joint ventures.” J. Constr. Eng.Manage. 139 (3): 304–311. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000619.

Littlechild, S. C., and K. G. Vaidya. 1976. “The propensity to disrupt anddisruption nucleolus of a characteristic function game.” Int. J. GameTheory 5 (2): 151–161. https://doi.org/10.1007/BF01753316.

Liu, J., Z. Wang, M. Skitmore, and L. Yan. 2019. “How contractor behavioraffects engineering project value-added performance.” J. Manage. Eng.35 (4): 04019012. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000695.

Lu, C., Z. Yu, X. Wang, and Y. Hong. 2020. “Empirical study on theobstacles to the success of joint ventures in construction projects.”Adv. Civ. Eng. 2020 (Jan): 12. https://doi.org/10.1155/2020/1748198.

Madani, K. 2010. “Game theory and water resources.” J. Hydrol. 381 (3–4):225–238. https://doi.org/10.1016/j.jhydrol.2009.11.045.

Matsumoto, A., and F. Szidarovszky. 2016. Game theory and its applica-tions. New York: Springer.

Mba, M. F. B., and J. N. Agumba. 2018a. “Critical success factors influenc-ing performance outcome of joint venture construction projects in SouthAfrica: Comparison of first and second order models.” Constr. Econ.Build. 18 (3): 74–94. https://doi.org/10.5130/AJCEB.v18i3.5885.

Mba, M. F. B., and N. J. Agumba. 2018b. “Critical success factors of jointventures in the construction industry: Literature review.” In Proc., 21stInt. Symp. Advancement of Construction Management and Real Estate,597–605. New York: Springer.

McIntosh, K., and B. McCabe. 2003. “Risk and benefits associatedwith international construction–consulting joint ventures in the English-speaking Caribbean.” Can. J. Civ. Eng. 30 (6): 1143–1152. https://doi.org/10.1139/l03-063.

Mikapagaro, N. A., D. N. G. A. K. Tesha, G. C. Maro, and B. K. Edson.2018. “The implementation of risk management strategies in joint ven-ture building projects in Dar Es-Salam, Tanzania.” Int. J. Eng. TrendsTechnol. 66 (3): 133–153. https://doi.org/10.14445/22315381/IJETT-V66P223.

Mohamed, S. 2003. “Performance in international construction jointventures: Modeling perspective.” J. Constr. Eng. Manage. 129 (6):619–626. https://doi.org/10.1061/(ASCE)0733-9364(2003)129:6(619).

Moulin, H. 2003. Fair division and collective welfare. London: MIT Press.Munns, A. K., O. Aloquili, and B. Ramsay. 2000. “Joint venture negotia-

tion and managerial practices in the new countries of the former SovietUnion.” Int. J. Project Manage. 18 (6): 403–413. https://doi.org/10.1016/S0263-7863(99)00071-X.

Myerson, R. B. 1991. Game theory: Analysis of conflict. Cambridge, MA:Harvard University Press.

Nakamura, M. 2005. “Joint venture instability, learning and the relativebargaining power of the parent firms.” Int. Bus. Rev. 14 (4): 465–493.https://doi.org/10.1016/j.ibusrev.2005.04.003.

Naylor, J., and M. Lewis. 2003. “Internal alliances: Using joint ventures ina diversified company.” Long Range Plann. 30 (5): 678–688. https://doi.org/10.1016/S0024-6301(97)00051-4.

Norwood, S. R., and N. R. Mansfield. 1999. “Joint venture issues concern-ing European and Asian construction markets of the 1990’s.” Int. J.Project Manage. 17 (2): 89–93. https://doi.org/10.1016/S0263-7863(98)00016-7.

Ott, U. F. 2006. “The rules of IJV games.” In Proc., Int. Joint Ventures:An Interplay of Cooperative and Noncooperative Games Under Incom-plete Information, 32–60. London: Palgrave Macmillan. https://doi.org/10.1057/9780230625464.

Ozorhon, B., D. Arditi, I. Dikmen, and M. T. Birgonul. 2008. “Implicationsof culture in the performance of international construction joint ven-tures.” J. Constr. Eng. Manage. 134 (5): 361–370. https://doi.org/10.1061/(ASCE)0733-9364(2008)134:5(361).

Ozorhon, B., D. Arditi, I. Dikmen, and M. T. Birgonul. 2010. “Performanceof international joint ventures in construction.” J. Manage. Eng. 26 (4):209–222. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000022.

Ozorhon, B., D. Arditi, I. Dikmen, and M. T. Birgonul. 2011. “Toward amultidimensional performance measure for international joint venturesin construction.” J. Constr. Eng. Manage. 137 (6): 403–411. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000314.

Perng, Y.-H., S.-J. Chen, and H.-J. Lu. 2005. “Potential benefits for collabo-rating formwork subcontractors based on co-operative game theory.”Build. Environ. 40 (2): 239–244. https://doi.org/10.1016/j.buildenv.2004.07.007.

Prasitsom, A., and V. Likhitruangsilp. 2015. “Managing risks in form-ing international construction joint ventures in Thailand.” Int. J.Constr. Eng. Manage. 4 (4): 106–121. https://doi.org/10.5923/j.ijcem.20150404.02.

Rasmusen, E. 2006. Games and information. Chicester, UK: Wiley.SELI Overseas. 2018. “Bergen point WWTP outfall replacement (New

York).” Accessed May 20, 2019. http://www.selioverseas.com/assets/seli-overseas---scheda_1.pdf.

Shapley, L. S. 1953. “A value for n-person games.” In Vol. 2 of Contribu-tions to the theory of games, edited by H. W. Kuhn and A. W. Tucker,307–317. Princeton, NJ: Princeton University Press.

Shen, L. Y., G. W. C. Wu, and C. S. K. Ng. 2001. “Risk assessment forconstruction joint ventures in China.” J. Constr. Eng. Manage. 127 (1):76–81. https://doi.org/10.1061/(ASCE)0733-9364(2001)127:1(76).

Shoubi, M. V., A. S. Barough, and O. Amirsoleimani. 2012. “Application ofcost allocation concepts of cooperative game theory approach in con-struction industry.” Res. J. Appl. Sci. Eng. Technol. 5 (12): 3457–3464.https://doi.org/10.19026/rjaset.5.4593.

Stolwijk, A. 2010. Solution concepts in cooperative game theory. Master'sthesis, Mathematical Institute, Universiteit Leiden.

Straffin, P. D. 1993. Game theory and strategy. New York: MathematicalAssociation of America.

Teng, Y., X. Li, P. Wu, and X. Wang. 2019. “Using cooperative game theoryto determine profit distribution in IPD projects.” Int. J. Constr. Manage.19 (1): 32–45. https://doi.org/10.1080/15623599.2017.1358075.

Tetteh, M. O., and A. P. C. Chan. 2019. “Review of concepts and trends ininternational construction joint ventures research.” J. Constr. Eng. Man-age. 145 (10): 04019057. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001693.

Viswanathan, S. K., and K. N. Jha. 2020. “Entry mode sequencing modelfor emerging international construction firms.” J. Manage. Eng. 36 (3):05020002. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000747.

von Neumann, J., and O. Morgenstern. 1944. Theory of games and eco-nomic behavior. London: Princeton University Press.

Walker, D. H. T., and D. S. Johannes. 2003. “Construction industry jointventure behaviour in Hong Kong—Designed for collaborative results?”Int. J. Project Manage. 21 (1): 39–49. https://doi.org/10.1016/S0263-7863(01)00064-3.

Xue, J., H. Yuan, and B. Shi. 2017. “Impact of contextual variables on ef-fectiveness of partnership governance mechanisms in megaprojects:Case of Guanxi.” J. Manage. Eng. 33 (1): 04016034. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000476.

Yan, M.-R. 2011. “A fuzzy logic enhanced bargaining model forbusiness pricing decision support in joint venture projects.” J. Bus.Econ. Manage. 12 (2): 234–247. https://doi.org/10.3846/16111699.2011.573281.

Yan, M.-R., and S.-T. Li. 2011. “A strategic bargaining decision supportmodel for project-based alliance.” In Proc., IEEE Symp. on Computa-tional Intelligence in Multicriteria Decision-Making 2011, 121–128.New York: IEEE.

© ASCE 04021016-12 J. Manage. Eng.

J. Manage. Eng., 2021, 37(3): 04021016

Dow

nloa

ded

from

asc

elib

rary

.org

by

Ara

b A

cade

my

For

Scie

nce

& T

ech

on 0

3/08

/21.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Yan, M.-R., C.-L. Lin, and W. Lo. 2006. “Bargaining strategies forconstruction joint ventures by fuzzy logic.” In Vol. 8 of Proc., 9th JointConf. Information Sciences (JCIS), 539–552. Paris: Atlantis Press.https://doi.org/10.2991/jcis.2006.287.

Yao, M., F. Wang, Z. Chen, and H. Ye. 2020. “Optimal incentivecontract with asymmetric cost information.” J. Constr. Eng. Manage.146 (6): 04020054. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001832.

Zhang, G., and P. X. Zou. 2007. “Fuzzy analytical hierarchy process riskassessment approach for joint venture construction projects in China.”J. Constr. Eng. Manage. 133 (10): 771–779. https://doi.org/10.1061/(ASCE)0733-9364(2007)133:10(771).

Zhao, X., B.-G. Hwang, and G. S. Yu. 2013. “Identifying the critical risksin underground rail international construction joint ventures: Case studyof Singapore.” Int. J. Project Manage. 31 (4): 554–566. https://doi.org/10.1016/j.ijproman.2012.10.014.

© ASCE 04021016-13 J. Manage. Eng.

J. Manage. Eng., 2021, 37(3): 04021016

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nloa

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elib

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by

Ara

b A

cade

my

For

Scie

nce

& T

ech

on 0

3/08

/21.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.