Secret Contracting in MultilateralRelations

Patrick Rey (Toulouse School of Economics)

Thibaud Vergé (CREST, ENSAE Paris, Institut Polytechnique de Paris)

CRESSE 2019 – Rhodes

Multilateral Vertical Relations

▪ IO theory models of vertical relations mostly focuson▪ Coordination problems within a given vertical structure with a

monopolist at the upstream and/or downstream level(s).

▪ Competition may be introduced through

▪ competing fringe suppliers/retailers; or

▪ rivalry among vertical structures (e.g., franchise networks)

▪ Yet in practice “interlocking” relationships arecommon▪ Aircrafts (GE, Pratt-Whitney, Airbus and R&R engines on Boeing and

Airbus aircrafts), PCs (Intel and AMD chips in most OEMs’ PCs), majorsbrands in supermarket chains, healthcare provision, media content onpay TV, etc.

Multilateral Vertical Relations

▪ But theory papers usually impose various restrictions▪ Set of feasible contracts, e.g., linear or two-part tariffs or quantity

forcing.

▪ Homogeneous input.

▪ Public tariffs

▪ Notable exception: Nocke and Rey (2018) with Cournot competition.

▪ Empirical analysis in need of an appropriate framework▪ Healthcare (lump-sum transfers or linear tariffs)

▪ Gowrisankaran et al. (2015), Ho and Lee (2017)

▪ Media: content / pay-TV (linear tariffs)

▪ Chipty and Snyder (1999), Crawford and Yurukoglu (2012), Crawford et al.(2015)

▪ Single or simultaneous bargaining (upstream and downstream)

▪ Limits strategic effect as altering one tariff has no impact on final prices.

This paper

▪ Flexible yet tractable framework▪ Arbitrary number of firms at each level, upstream and downstream

differentiation (and asymmetry), balanced bargaining power in bilateralrelations, general non-linear tariffs, “full impact” on final prices.

▪ Secret contracting and contract equilibrium (Nash-in-Nash)

▪ See micro-foundation: PBE of a delegated negotiations game.

▪ Initial choice of partners / endogenous network of relationships.

▪ Can then be used to study▪ Competitive impact of vertical restraints

▪ RPM (min/max RPM), price parity and MFN clauses, resale vs. agency.

▪ Impact of mergers on prices and network

▪ Nature of contracts

▪ Public or secret contracting

▪ Linear vs. non-linear tariffs, exclusivity clauses, etc.

Framework

▪ Successive oligopoly with (asymmetric) differentiation atboth levels and (asymmetric) constant unit costs.

pnm

t11 tnm

tn1

M1

Customers

t1m

Mn

R1 Rm

cn

γm

c1

γ1

qij = Dij(p11,…,p1n,…,pn1,…,pnm)

p1mpn1

p11

…

…

Bargaining equilibrium

▪ Timing▪ Each upstream firm negotiates a non-linear tariff with each

downstream firm (negotiations are simultaneous and secret).

▪ Each retailer observes its own tariffs and sets its prices (pricingdecisions are simultaneous).

▪ Contract equilibrium with Nash bargaining▪ Contract equilibrium: When an upstream-downstream pair negotiates,

it takes all other equilibrium tariffs as given.

▪ Nash bargaining: Balanced bargaining to split the surplus generated bya successful negotiation.

▪ “Nash-in-Nash” / passive beliefs

Equilibrium analysis

▪ There exists an equilibrium in two-part tariffs▪ “True equilibrium”: no restriction on tariffs.

▪ “Cost-based” tariffs, i.e., wholesale price equal to marginal cost.

▪ Upstream firms obtain a positive profit but downstream firms obtainmore than “their” share of the profit.

▪ Retail prices are “almost” uniquely defined▪ “Smooth equilibria”: tariffs are differentiable and internal-best

responses are also differentiable.

▪ Multiple equilibria with different divisions of profits▪ Intuition: limiting retailer’s freedom in case of break-down (e.g., convex

tariffs).

▪ Unique equilibrium in two-part tariffs.

Micro-foundation

▪ General non-linear tariffs▪ With lump-sum transfers (e.g., Collard-Wexler et al. (2019)), the tariff

does not affect the “pie” only the way it is shared.

▪ Here, (marginal) wholesale prices affect retail prices and profits.

▪ Not a problem with Cournot competition (see Nocke and Rey, 2018).

▪ Multi-sided deviations problematic with Bertrand competition (see Rey andVergé, 2004).

▪ Solution: delegated negotiations.▪ Each upstream (downstream) firm has m (n) different agents, one for

each downstream (upstream) firms.

▪ Each pair of delegated agents negotiates a tariff (e.g., random selectionof who gets to make a take-it-or-leave-it offer); each retailer thenobserves the contracts signed by its agents and sets its prices.

Micro-foundation

▪ Look for sequential equilibria of this game▪ m x n players in stage 1 (tariffs), m players in stage 2 (retail prices).

▪ Consistent beliefs: “don’t signal what you don’t know”.

▪ Bargaining power does not affect pricing incentives.▪ Partners can share their bilateral joint- profit (e.g., fixed fees) and thus

want to maximize this joint-profit regardless of which side gets to makean offer.

▪ Equivalence result▪ For any bargaining equilibrium, there exists an equivalent sequential

equilibrium of the delegated negotiations game.

▪ Conversely, any sequential equilibrium with regular price responsesand tariffs is a bargaining equilibrium.

Endogeneous network

▪ “Nash-in-Nash” implies that all channels are always active.▪ Yet a manufacturer may be better-off under exclusivity.

▪ Preliminary stage to endogenize the distribution network▪ Manufacturers and retailers simultaneously announce which channels

they want, a channel is established if both parties agree.

▪ Continuation equilibrium: unique equilibrium in (cost-based) two-parttariffs for any channel network.

▪ Focus on coalition-proof Nash-equilibria (see Bernheim et al., 1987).

▪ Example: successive symmetric duopolies▪ 2 manufacturers, 2 retailers, marginal costs normalized to 0.

▪ When needed, restriction to the following (linear) inverse demandfunction: ( ) ( ) ( ), , , = 1 , where , 1ij hj ik hk ij hj ik hkP q q q q q q q q − + − +

Endogeneous network

Brand substitution

Retailsubstitution

Exclusive DealingA B

1 2

InterlockingRelationships

A B

1 2

Mergers

▪ Impact of a merger▪ Price effects: classic analysis.

▪ “Network effects”: a merger may affect the distribution network

▪ Horizontal mergers▪ Downstream: can expand the equilibrium network and benefit

consumers despite anticompetitive price effects.

▪ Upstream: can instead trigger (partial) vertical foreclosure and harmconsumers (or society) even though no (direct) price effects.

▪ Vertical merger▪ Integrated supplier raises marginal price to the downstream rival.

▪ Impact on network can go both ways.

▪ Overall effect is more often negative.

Downstream merger

Retailsubstitution

Brand substitution

Upstream merger

Retailsubstitution

Brand substitution

Vertical merger

Retailsubstitution

Brand substitution

More

▪ Public contracting▪ Same timing as before except that all negotiated tariffs become public

before downstream pricing decisions.

▪ Similar micro-foundation: delegated negotiations.

▪ Agents observe only their own bilateral negotiation but retailers haveobserved all tariffs when they compete in prices.

▪ Focus on subgame-perfect equilibria

▪ Assuming delegated negotiations avoids multilateral deviations but alsomultilateral responses to unilateral deviations (see Rey and Vergé,2010).

▪ Focus on two-part tariffs (potential issue with non-existence if tariffsare sufficiently concave).

▪ Successive symmetric duopoly case: wholesale prices above costs butretail prices below the monopoly level.

Even more – Verticals

▪ Resale price maintenance▪ Multiple equilibria, in particular firms can sustain monopoly prices

(even with purely bilateral RPM agreements).

▪ Prices floors (caps) are needed if there is more substitution amongbrands (stores).

▪ Price parity – MFN clauses▪ Agreement that retailers charge the same prices for the different

brands that they carry.

▪ Here such agreements do not affect prices but only profit sharing.

▪ Agency model▪ Same analysis “upside-down” (suppliers are now downstream,

platforms upstream providing services).

Next steps

▪ Endogenizing adoption of vertical arrangements (andnetwork formation)▪ E.g., RPM affects price levels and industry profits, but also profit sharing

(differently with min or max RPM).

▪ But it may also affect the distribution network as well.

▪ Similar issue for resale vs. agency model.

▪ Investment, innovation, entry, etc.

▪ Others???

Patrick Rey (patrick.rey@tse-fr.eu)

Thibaud Vergé (thibaud.verge@ensae.fr)