Chris Starmer

1. Chris Starmer Day 4 - Experimental Games TSU Short course in Experimental and Behavioural economics, 5-9 November 2012

2. Route Map Part 1: • Modelling social/strategic interaction as ‘games’ • Some basic ideas in game theory • From theory to empirics • What people do and how to do well Part 2: • Identifying Social Preferences • The impact of Social Preferneces

3. Preferences Game theory One of the main tools of modern econ analysis Models strategic interaction through stylised ‘games’ e.g. prisoner’s dilemma……..

4. The Background Story • Two people arrested on suspicion of a crime • Police not enough evidence to convict • Idea – place in separate cells (no communication) • Each has two options (confess or silent) • Consequences…………

5. Consequences for each depend on actions of both • If both confess: • Each get Moderate/High sentence (6 years) • If neither confess: • Each get Moderate/Light sentence (3 Years) • If one confesses while other remains silent • Confessor – gets very light sentence (1 year) • Silent gets very harsh sentence (10 Year)

6. In game theory, analysis just requires the RANKING of payoffs That is, we translate from the absolute material payoffs to ordinal rankings

7. Consequences for each depend on actions of both • If both confess: • Each get Moderate/High sentence (6 years) [2] • If both remain silent: • Each get Moderate/Light sentence (3 Years) [3] • If one confesses while other remains silent • Confessor – gets very light sentence (1 year) [4] • Silent gets very harsh sentence (10 Year) [1]

8. Interpreting Payoffs • These red numbers are called ‘utilities’ • They represent each player’s own ranking of the possible outcomes of the ‘game’ • For the game to be correctly specified, these ranking should include consideration of everything that the players care about • E.g. if there is ‘honour among thieves’ so they hate to confess, this should be reflected in ranking (and might change the rankings on previous slide)

9. Normal Form • Now represent the game in ‘Normal Form’ • Matrix • One player selects rows • Other selects columns

10. Prisoner’s dilemma Player 2 - Marina Silent Confess 1,4 3,3 Silent Player 1 - Rati 4,1 2,2 confess (utility) payoffs in each cell with Row (Rati) written first in each pair

11. What will be the outcome of this game? • What does game theory predict rational players would do? • What do ordinary people do in situations like this? • Will look at both of these questions but first………..

12. What would you do? Player 2 - the other prisoner Silent Confess STAY SEATED Silent 1,4 3,3 4,1 STAND UP Confess 2,2 To help you – I’ve highlighted your (row) payoffs in RED

13. Now the game theory prediction Very simple for this game

14. Game Theoretic Prediction Player 2 - Marina Dominant Strategy Confess silent 1,4 3,3 silent Player 1 - Rati 4,1 2,2 confess Dominant Strategy (utility) payoffs in each cell with Row (Rati) written first in each pair

15. NOTICE Player 2 - Marina Silent Confess 1,4 Silent 3,3 Player 1 - Rati 4,1 2,2 Confess The predicted outcome is (Pareto) SUBOPTIMAL - at the predicted outcomes, both players are worseoff than they could have been

16. 3 cheers for rational choice theory • This simple game demonstrates the power of rational choice analysis….. • It captures a fundamental insight of social science. • It is a mistake to assume that individual pursuit of self-interest fosters the good of all • Pursuit of rational self interest can lead to outcomes which are worse for all than others available • Maybe models many important social problems (e.g. pollution control, arms races etc.)

17. Real play When real people play experimental games with payoffs structured so that they would be prisoner’s dilemma’s IF all they cared about was money payoffs they often manage to reach the pareto-superior outcome…….

18. In games with Money payoffs, people often reach the better joint payoff Player 2 - Marina Silent Confess 1,4 Silent 3,3 Player 1 - Rati 4,1 2,2 Confess

19. How do they escape the dilemma? • Happy ignorance? • They don’t understand the game • Enlightened reasoning? • E.g. Schelling reasoning • They have “social preferences”? • They don’t care just about the money • They care about each other’s outcomes • Players think of the game as part of an ongoing social game Part 2 Next

20. 2. Repeated Games • Would things be different if people play a PD game repeatedly? • Reputation building • GT tells us: • If PD games is one shot no opportunity for rational players to develop cooperative reputations • Repeated Game: can be Much More Complex and support cooperative strategies

21. Robert Axelrod’s (book)The Evolution of Cooperation • Cooperation emerges spontaneously in the world in surprising places • e.g. trench warfare • Axelrod’s question • What’s the best strategy for playing the repeated prisoner’s dilemma? en.wikipedia.org/wiki/Evolution_of_cooperation

22. Axelrod’s Tournament • Invited game theorists to participate in tournament • Repeated prisoner’s dilemma • Each participant submitted a strategy • Strategy, specifies ‘Coop’ or ‘Not’ for each round • can use history of moves to determine choice in any round

23. Round Robin • 14 entries submitted, all by ‘professionals’ • Strategies coded as computer programmes • Every strategy played repeated PD against: • every other strategy • itself • random (plays coop/not with p=0.5) • Each pairing played • 200 rounds • repeated 5 times (average performance)

24. The winner • Anatol Rapoport (Univ. Toronto) • Tit-for-Tat • first round: coop • subsequent rounds: copies opponents play in previous round

25. Why was TFT successful? • A single characteristic distinguished high from low-scoring strategies…. • Being ‘NICE’? • NICE means; • don’t be the first to defect • cooperating in first round • Large gap between average scores of nice and not-nice strategies

26. Why did nice rules do well? • Because of the environment • Nice rules score highly when they meet • (they cooperate all the way through) • And, • there were enough nice rules around for them to raise each other’s scores

27. Which Nice Rules Did Best? • Most successful nice rules tended to be ‘FORGIVING’ • Forgivingness • is willingness to resume cooperation after the other player has failed to cooperate. • Notice: TFT is forgives rapidly • TFT resumes cooperation as soon as it observes the other player doing so

28. Why is it good to be forgiving? • Compare with another nice but non-forgiving strategy…. • TRIGGER • Cooperates until it observes non-cooperation • then will never cooperate again • This strategy does: • well with other nice rules • But with non-nice rules, once a non-cooperative move happens, there is never any future cooperation

29. Axelrod’s advice for playing repeated PDs • Don’t be envious • don’t try to beat the other player • can only do this by actions which will undermine cooperation and joint payoff max • Don’ t be first to ‘cheat’ • Reciprocate cooperation and cheating • Don’t be too clever! • Cooperation is helped by people understanding your behaviour

30. Concluding Observations • GT predicts the behaviour of real people (worryingly) well in some settings • e.g. one shot, high payoff. • Cooperation may be more viable when there is repetition • what it is optimal to do depends on the environment

31. Session 4 – Part 2 Social Preferences

32. People care about each others outcomes “participants in experiments frequently choose actions that do not maximise their own monetary payoffs when those actions affect others’ payoffs. They sacrifice money in simple bargaining environments to punish those who mistreat them and share money with other parties who have no say in allocations” (Charness and Rabin, QJE 2002, p817)

33. Evidence • Some of the early and most famous experimental evidence supporting this claim comes from studies using: • The Ultimatum game

34. Ultimatum Game • Two players have to divide a fixed pie p • Player 1 (the proposer) proposes a division • (x, p-x) x = proposer’s share • Player 2 (the responder) observes the offer and either accepts or rejects. • If she accepts the agreed upon division is implemented • If she rejects both players get nothing

35. Game theoretic prediction Standard assumptions: • Both players are rational, i.e. everyone maximizes only his/her monetary income Standard analysis (‘Backward induction’) • Player 2 will accept any positive offer • So, Player 1 will offer the smallest possible positive amount to player 2

36. Stylised Facts from UG Expmts • Play deviates (systematically) from GT predictions: • close-to-even splits are often proposed • ‘low’ offers often rejected

37. Specific StudyGüth, Schmidtberger, Schwarze (1982, JEBO) • Pie size varied from 4 to 10 DM • Subjects were in one room, but no subject knew the person with whom he/she was paired • Real monetary stakes Two treatments • “Naive” (inexperienced) subjects • Experienced subjects: Same experiment one week later with same subjects

38. Ultimatum game experiments Güth, Schmidtberger, Schwarze (1982, JEBO) • Results • “Naive” subjects • Modal offer: 50% of the pie (7 of 21) • Mean offer: 37% of the pie • Experienced subjects • Mean offer: 32% of the pie • 2/21 offer 50% • Systematic deviation from game theoretic prediction GSS conclude: Game theory is “of little help in explaining ultimatum game behaviour”

39. What happens when stakes rise? Cameron (1999, Econ Inquiry) Experiments in Indonesia pie = from Rupiah 5000 (≈ $ 2.5) to R200 000 (≈ $ 100) R 200 000 ≈ 3 x average monthly expenditure • Results: • Offers approach 50/50 with increasing stakes • Responders more willing to accept a given percentage in higher stakes games

40. What accounts for this behaviour? Two possible explanations: • Fairness, Altruism • Strategic concerns, fear of rejections • This has been investigated using ‘Dictator Games’………

41. Dictator versus Ultimatum Games Forsythe, Horowitz, Savin and Sefton (Games and Economic Behavior, 1994) Dictator Game: Proposer decides on division (x, p-x), responder has no choice but to accept. • If concerns with fairness fully explain behaviour, the distribution of offers should be the same in both games

42. Dictator versus Ultimatum Game Results:Source Fig 4.4. Forsythe, et al. 1994. Results suggest UG behaviour reflects a mix of altruistic and strategic concerns

43. An application of Social Preferences Voluntary Contributions to Public Goods

44. Public Goods • (Pure) Public good • Once provided everybody benefits • Can’t exclude people from the benefit • Examples: Street lights, National defense • Standard economic analysis • PGs may not be provided by market because, self-interested individuals will not pay • (free ride)

45. Public Goods Experiments • Voluntary Contribution Mechanism • N Individuals; each allocated T tokens • divide between ‘private’ vs ‘public’ account • Public contributions raised by factor m • Each individual (i) receives payoff: πi = T – ci + (m/N).(∑contributions) • with 1 < m < N • full contribution (social optimum) • zero contribution (individual optimum)

46. Public Goods Experiments findings • Marwell & Ames (J. Pub Econ, 1981) • On average 40-60% contribution • except economists  • Most people are willing to contribute than theory (as usually interpreted) predicts

47. Subsequent work on Public Goods Lots of experimental research on PGs using VCM. Two significant dimensions include experiments exploring: • Repetition • Role of social sanctions • Opportunity to punish ‘free riders’

48. Repeated Play in VCM • When groups play the PG game repeatedly • Contributions go down toward the game theory prediction (based on private money maximisation)

49. The role of social sanctions Fehr and Gächter, (AER 2000) • a very influential experimental finding. Used a repeated VCM but; • modified to allow group members to sanction (i.e. punish) ‘free riders’.

50. Design (Fehr and Gächter, AER 2000) 2-stage game: 1st stage: standard Public good game 2nd stage: punishment stage Each member learns contribution of others Can then assign punishment points A punishment point costs the punisher 1 point and reduces the punished member’s payoff by 3 points. • (Perfect stranger design) • Punishment is second order public good • GT Prediction: no punishment, no contributions