ALEXIS BELIANIN and MARCO NOVARESE ICEF SU-HSE University of Piedmont

1. TRUST, COMMUNICATION AND EQULIBRIUM BEHAVIOURIN PUBLIC GOODS GAME: A CROSS-COUNTRYEXPERIMENTAL STUDY ALEXIS BELIANIN and MARCO NOVARESE ICEF SU-HSEUniversity of Piedmont Prepared for the IAREP-SABE meeting, 7 july 2006

2. 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

3. 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

4. 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.

5. 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).

6. 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)

7. 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

8. 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

9. Experimental design

12. 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

18. 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

20. 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

21. PG game, 1997

22. 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

23. 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 everyperiod 2, 3…, at most half of the total capital ofthe other players will be investedon 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.

24. 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

25. 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.

26. PG game as a Game Finite dynamic game of incomplete information Γ={Y,Z,>,N,I,A,(ui)i=1N,} • Histories of the game htHt • 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)

27. 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.

28. Solution • Take two copies of the universal belief space  with Borel -algebra F. Hence (,F ) is a Polish space (complete separable metric) • The first copy (,F ) corresponds to factual state space, the second (E,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

29. 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,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.