TRUST, COMMUNICATION AND EQULIBRIUM BEHAVIOUR

IN PUBLIC GOODS GAME: A CROSS-COUNTRY

EXPERIMENTAL STUDY

ALEXIS BELIANIN and MARCO NOVARESEICEF SU-HSE University of Piedmont

Prepared for the IAREP-SABE meeting, 7 july 2006

Summary

• Experimental study of cooperation and communication

• Cross-country comparison (Italy - Russia)• Players from different counties play

together in real time through Internet-based experimental website set up at ICEF (http://mief.hse.ru).

• Outline of a theory of equilibrium behaviour in public goods experiment

The public good (PG) game: Voluntary contribution mechanism

w – endowment

ci – contribution to public good (account )

n – number of group participants

w - ci – income from private account

k ici – income from public account accrued to every group member (k<1<kn)

Individual per period utility is

n

i iii ckcwcu1

)(

PG game: standard theory

• k<1 => equilibrium individual contribution is zero• 1<kn => socially efficient contribution is w• Prisoner dilemma structure of the game implies

that the equilibrium contribution to public account is zero in any single-stage game

• Backward induction implies the same result for any finitely repeated version of the game.– This result does not hold for an infinitely repeated

game with discounting (the Folk theorem)• Economic theory predicts that people will free-

ride, bringing contributions to public account down to zero.

PG game: evidence

• People are significantly more cooperative than theory predicts: initial contributions are about 50% (Marwell and Ames, 1979; Isaac e.a.,1984)

• Contributions decrease with repetitions and experience (Ledyard, 1995)

• Contributions increase with group robustness (partners vs. strangers treatments - Andeoni (1988), Palfrey and Prisbrey (1996)

• Basic findings are robust across countries and reward schemes (Henrich e.a., 2001).

Explanations

• Random errors (in voluntary contributions - Anderson e.a., 1998)

• Altruism or warm-glow (Palfrey and Prisbrey, 1997; Goeree e.a., 1999; Carter e.a., 1992)

• Conditional cooperation (Keser and van Winden, 2000; Levati, 2002)

• Utility of reciprocity or fairness (Rabin, 1993)• Inequality aversion (Fehr and Schmidt, 1999) or

justice considerations (Fehr and Gächter, 2000)

Experimental setup• Game parameters: n=6, w=10, k=1/3• 12 rounds in each treatment• 3 sessions

– Italian participants only (12 players)– Russian participants only (12 players)– Mixed Italian and Russian participants (24 players)

• Subjects – students of Law and Economics Università del Piemonte Orientale at Alessandria, Italy; and students of economics at International College of Economics and Finance, Russia.

• Incentives – percentage points to course grades in Italy and Russia

Effects• Cross-country differences

– Separately across countries (Italy and Russia)– Within the same game (does it matter that

players know their opponents came from different country?)

• Communications effects (play before and after cheap talk)

• Gender effect– Within country– Across countries

Experimental designTreatmentGroups Game 1 (no cheap-talk)

Game 2 (preceded by cheap-talk)

A Mix males Italian males-femalesB Mix females Russian males-femalesC Italian males-females Mix males-femalesD Russian males-females Mix males-females

Single-country sessions (gender identities known)Game 1 Game 2 Game 32 Male-female groups, no cheap talk

2 Male-female groups, preceded by cheap talk

All-male and all-female group, no cheap talk (but experience of games 1 and 2)

Procedures

• Allocation of subjects• Reading instructions, answering questions• Game 1 (subjects are advised to keep record of

their play and performance)• Cheap talk session (20 minutes in the forum

integrated with the experimental session)• Game 2• (in Italian and Russian sessions) Relocation of

players by gender and Game 3

Observations• Significant contributions• Relatively weak decrease in contributions• Strategic behaviour (drops in cooperation

in the last periods)• No significant differences across countries• Significant effect of cheap-talks in cross-

country sessions (and no significant effect in single-country sessions)

• Higher volatility of contributions in Russian sessions

Gender effect

• Russian females tend to be significantly more cooperative than Russian males– Self-supporting increase of cooperation

among Russian females

• No analogous findings for Italy, as well as for other countries (Holt and Laury, 1997).

• Robustness of this finding across time and experimental designs

PG game, 1997

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 1 2 3 4 5 6 7 8 9 10 11

Periods

% c

ontr

ibut

ions

MSU 8F,money,commun

HSE 8F,money,priv

HSE 4M/4F,money,priv

MSU 4M/4F,money,commun

MSU 6M/2F,money,commun

EMSCH 7M/1F,imag,priv

MIIT 8M,priz,priv

Conclusion

• Similar pattern of contributions in all three sessions (Italian, Russian and mixed)

• Effect of cheaptalk in cross-country sessions• Higher variance of bids for the Russians vis. the

Italians• Significant gender effect for the Russians• More evidence needed: (welcome to join!:)• Need for a theoretical framework to explain real

behaviour of individuals in PG game

Theory: a first look• Payoff function 10 - ci + ci /3, 10 players, 10 periods.• Suppose in the first period the nine players choose

ci=10, and consider decision of the last player №10• Case 1: Player 10 believes that the others will set ci=10

provided no one defects; if someone defects, they immediately switch to ci=0 forever.– This trigger strategy warrants c10=10 (everything to public account), as

33.33 · 10 = 333.3 > 40 + 10 · 9 = 130• Case 2: Player №10 believes that in the first period all others

play ci=10, and in every period 2, 3…, at most half of the total capital of the other players will be invested on public account– It is better to defect always, c10=0, rather than c10=10, as

33.33 + (45+10)/3 · 9 = 198.33 < 33.33+(10+45/3) · 9 = 258.33 < 40+(10+90/(2 · 3)) · 9 = 265.

• In general, optimal action of the players depends on the beliefs about each others’ actions.

Theory: qualifications

• Rationalistic theory: does not incorporate any moral sentiments.

• Optimal behaviour is the one which maximizes individual expected payoff in the dynamic PG game– Standard neoclassical/game theorist view

• Rational behaviour is the one which gives directions towards reaching maximum payoff– Procedural rationality viewpoint

• Definitions are not contradictory: they just emphasize different aspects of preference towards higher reward

Observation

• The inference of player i about future

actions of the opponents is based on her perception of the rationality of the other players, which need not the be the

same as the actual rationality of these other players.

PG game as a GameFinite dynamic game of incomplete information Γ={Y,Z,>,N,I,A,(ui)i=1

N,}•Histories of the game htHt

– In the PG game, observed histories are not the same as actual ones: each player knows only his past actions and the statistics of those of the others

•Information structure of the game Γ:X0

= HT – set of all possible histories over T periods Recursively, Xj+1= Xj ΔΠiXj, beliefs over possible

histories Universal state space = X0 ΠiX, a product of

physical uncertainty and all types of the players (= imbedded sequences of probability distributions)

Problem• Standard way to derive equilibrium in this

settings is to use beliefs for each type derive

• This derivation is not applicable subject to the Observation we made, because beliefs of each player about others’ behaviour (which depends on their beliefs) need not be consistent with their actual beliefs that govern this behaviour.– In terms of the theory, neither common prior over

nor common knowledge of can be assumed.

i i

*i i i i -i

s

s = arg max ( ) u (s ( ), s ( ), )d( )S

Solution

• Take two copies of the universal belief space with Borel -algebra . Hence (,) is a Polish space (complete separable metric)– The first copy (,) corresponds to factual state

space, the second (E,) – to believed state space

• The space of individual uncertainty about factual and believed states is given by all continuous maps : E E from the Borel product set.

• This space on E generated by this mapping is called analytic, or Souslin. Mapping is called theory of player i in period t=1,2…T

Main results

• Strategies of players are measurable mappings from analytic spaces to the set of strategies.

• For every strategy in S there exists a unique belief defined on the set (E,)

• A player is called rational if his sequence of mappings from beliefs to actions in each stage game are filtrations on the sequence of beliefs.

• The limit set of strategies defined by the theory of a rational player exactly coincides with the set of rationalisable strategies in the PG game.