Economics 776: Experimental Economics First Semester 2007 Topic 2: Norms and Preferences: Evidence

1. Economics 776:Experimental EconomicsFirst Semester 2007Topic 2: Norms and Preferences: Evidence Assoc. Prof. Ananish Chaudhuri Department of Economics University of Auckland

2. Other-regarding preferences • The null hypothesis of game theory is the homo economicus assumption of self-interest • But it turns out that in a large majority of cases people exhibit what might be called other-regarding preferences • Altruism • Fairness • Emotions play a role in economic decisions

3. Ultimatum Game • Ultimatum Bargaining Game with a pie of $c • Player 1 offers an allocation (c-x,x) where x is the amount offered to Player 2. • Player 2 is informed about the offer and can accept or reject. • If player 2 rejects both players earn zero. • If player 2 accepts the proposed allocation (c-x,x) is implemented. • Self-interest prediction: (c-,), with   0, is proposed and accepted, as is every offer x > .

4. Dictator Game • Dictator Game • Like the ultimatum game but player 2 has no choice so that the proposed allocation is always implemented. • Self-interest prediction: (c -,) where   0 is proposed.

5. The ultimatum game (Güth, Schmittberger and Schwarze, JEBO 1982) • Split DM 4 or DM 10 (multiples of DM 1) • inexperienced subjects • All offers above DM 1 • Modal x = 50 percent of pie (7 of 21 cases) • Mean x = 37 percent of pie • A week later (experienced subjects) • All except one offer above DM 1 • 2/21 offer an equal split • Mean offer 32 percent of pie • 5/21 of the offers are rejected • Systematic deviation from standard prediction

6. Do higher stakes change the results? • Hoffman, McCabe, Smith (1999): Ultimatum Game with 10$ and 100$ • Offers are not dependent on the size of the cake. • Rejections up to 30$ • Cameron (1995): UG in Indonesia 2.5$, 20$, 100$ (GDP/Person = 670$) • The higher the stakes the more offers approach 50/50. • Responders more willing to accept a given percentage offer at higher stakes. • Without payments we see differences: less generous offers and more rejections.

9. Does altruism explain the high first mover offers? • Forsythe, Horowitz, Savin and Sefton (GEB 1994) compare simple ultimatum games with dictator games. In the latter, the proposer proposes a division (1-x,x) of the bargaining cake, which is then implemented. • Result 1: • In the dictator game the distribution of x shifts significantly towards x = 0 relative to the ultimatum game if real money is at stake (modal offer is x = 0). • If only hypothetical questions are asked no such shift can be observed.

10. Does altruism explain the high first mover offers • Result 2: • Even with real pay there is a concentration of offers around the equal split (see Fig. 4.4) • Conclusion: Some of the subjects seem to be motivated by altruism but the higher concentration of offers around the equal split in the ultimatum game suggests that behavior cannot be fully attributed to altruism.

12. Social distance • Conjecture that experimenters exert a kind of social control merely by being able to observe subjects’ actions. • Hoffman, McCabe and Smith (1999) report that if it is ensured that subjects know that the experimenter cannot observe individual decisions approximately 70 percent of the subjects in the dictator game give nothing and almost no offers above 0.3 can be observed. • And: does such an environment itself lead to some sort of experimenter effect?

13. Social distance • Comparison of one-period ultimatum games with and without subject-experimenter anonymity (but always subject-subject anonymity). • Comparison of one-period ultimatum game with the impunity game which has the same move structure as the ultimatum game but the same incentive structure as the dictator game (for first mover).

14. Social distance • Impunity Game: Player 1 proposes a division (1-x, x) • Player 2 accepts or rejects. In case of rejection player 2 gets nothing while player 1 still gets 1-x. • Punishment option is removed.

15. Social distance (Bolton and Zwick 1995) • Punishment hypothesis: First movers in the ultimatum game choose “high” offers because of the fear of rejection. • Prediction: Lower offers in the impunity game compared to the ultimatum game. • Anonymity hypothesis: First movers in the ultimatum game do not want to be judged by the experimenter to be greedy and selfish. • Prediction: With subject-experimenter anonymity there are significantly lower offers than without subject-experimenter anonymity in the ultimatum game.

16. Player 1 Bottom Top Player 2 Player 2 Right Left Right Left 1 2 0.00 0.00 2.00 2.00 0.00 0.00

17. Social distance (Bolton and Zwick 1995) • Choices for the payoffs: • 2.20, 1.80 • 2.60, 1.40 • 3.00, 1.00 • 3.40, 0.60 • 3.80, 0.20 • Three conditions: • Ultimatum • Double Blind • Impunity (which removes the punishment option for Player 2)

18. Social distance (Bolton and Zwick 1995) Player A Equilibrium actions Equilibrium Outcomes (%)

19. Rejections rates by second mover In the Impunity Treatment no offer was turned down by the second movers, not even one of $0.20

20. Social distance • Results: • Punishment confirmed • Anonymity rejected • In the ultimatum game offers in the first five periods are slightly lower under anonymity, in the second five periods they are slightly higher. In general offers are similar to other non anonymous ultimatum games.

23. The Trust GameBerg, Dickhaut and McCabe (1995) • Player 1 and 2 are endowed with $10. • Player 1 decides how much of her $10 to transfer to player 2. • Experimenter triples any amount sent. • Player 2 is informed about 1’s transfer and decides how much of the tripled transfer to send back. • Standard prediction (using backward induction): • Player 2 sends back nothing. • Player 1 sends nothing.

25. Treatment 1 (No history) 32 pairs

26. Treatment 2 (Social History) 28 pairs

27. Does the trust game really measure trust? (Gneezy, et al., 2000) • Vary the upper bound on repayment amounts • If no repayment possible then this is the same as a dictator game except any amount sent gets multiplied by three • If more amount sent when the upper bound on repayments is higher then this would indicate that senders motivated by trust and expected reciprocation rather than a desire to “share” (or similar altruistic motives)

28. Does the trust game really measure trust? (Gneezy, et al., 2000) • Initial endowment of 10 chips • Any amount sent (a) is doubled to 20 • Receivers can send back (r) • Three treatments which vary the upper bound on r • r = 2 • r = 10 • r = 18

30. Does the trust game really measure trust? (Gneezy, et al., 2000) • Except for r = 2, resulting in the dictator game, higher contributions trigger higher repayments.

31. Does the trust game really measure trust? (Chaudhuri and Gangadharan (2005)) • Compare behaviour in a trust game with that in a dictator game • Within subjects treatment • 100 subjects • $10 initial endowment • Each play as sender and receiver • In the absence of trust there should be no difference in the amount sent as the Proposer in the trust game and the Allocator in the dictator game

32. Does the trust game really measure trust? (Chaudhuri and Gangdharan, 2005)) • Average amount sent in the trust game is $4.33 • Average amount sent in the dictator game is $1.345 • Significant difference using a t-test or a non-parametric Wilcoxon paired sign-rank test

34. Proposer’s decision and risk attitudes • Suppose the proposer decides to send $X out of his initial endowment of $10.00 to the responder. • The responder then gets $3X. • With probability “p” he returns “” proportion of that amount and with probability “1-p” he returns nothing. • So with probability “p” the proposer gets (10-X+3X) while with probability “1-p” he gets (10-X).

35. Proposer’s decision and risk attitudes • The expected payoff is E() = p(10-X+3X) + (1-p)(10-X) = 10 – X + 3pX (1) • Taking the derivative of expected payoff with respect to X we get (2)

36. Proposer’s decision and risk attitudes • Thus the expected payoff is increasing in X if and only if 3p > 1. • If 3p < 1 or p < 1/3, then from (2), the expected payoff is negative. In that case the proposer is better off simply holding on to the initial endowment. • Using “U” to denote the expected utility (with U(0) = 0), we can express the expected utility of the proposer in this case as E(U) = p*U(10-X+3X) + (1-p)*U(10 – X)

37. Proposer’s decision and risk attitudes • Proposer chooses X to maximize expected payoff • FOC: (3-1)pU’(10-X+3X) = (1-p)U’(10 – X) • Let the utility function exhibit constant relative risk aversion with the form • U(W) = • where  = coefficient of relative risk aversion. A larger value of  signifies a greater degree of risk aversion.

38. Proposer’s decision and risk attitudes • Using this CRRA utility function and substituting in the first order condition above we get or or

39. Proposer’s decision and risk attitudes • Taking the derivative of X w.r.t. the risk aversion parameter () we get where or (3)

40. Proposer’s decision and risk attitudes • The sign of the derivative depends on the value of log K • negative if log K is positive • positive if log K is negative. • If log K is negative that implies that < 1 or 3p <1 or p <1/3

41. Proposer’s decision and risk attitudes • This would be true if and only if a subject sends money expecting to get back less than 1/3 of what the responder gets • On the other hand, for those subjects who wish to maximize their payoff, log K must be positive, i.e. K > 1 i.e. or p > 1/3

42. Proposer’s decision and risk attitudes • For these subjects p > 1 and Log K > 0 and so the sign of the derivative in equation (3) is negative, i.e. the amount of money sent is decreasing in  • The higher the risk aversion parameter the smaller is the amount sent.

43. Proposer’s decision and risk attitudes • 44 people expect to get back less than 1/3 of what the receiver gets; on average sent $2.14 out of $10.00. • The modal amount (18 out of 44) sent by these subjects is $0.00. • 37 people expected to get back more than 1/3; average amount sent is $6.05. • 17 people expected to get back exactly 1/3; on average sent $5.41. • Average for those who expect to get back at least 1/3 or more is $6.05. • The modal amount sent is $10.00 (n = 17)

44. Amount Sent in the Trust Game Broken up by Gender On average men (n = 47) send $5.30 while women (n = 53) send $3.47

45. Chaudhuri and Gangadharan, 2005 • Amount of money received by the responder from the paired proposer and the percent of money sent back highly correlated. (Spearman’s Correlation Coefficient = 0.3203, p = 0.0033) • Responder (second) stage of the trust game is analogous to a dictator game. • Average amount sent as the allocator in the dictator game is 11.8% • Average amount returned as the responder in the trust game is 17.4%. • (significant at the 5% level using non-parametric Mann-Whitney U test /Wilcoxon ranksum test)

46. Chaudhuri and Gangadharan, 2005 • Responses regarding amount to be sent back using “strategy method” highly consistent with actual amounts sent back

48. Chaudhuri and Gangadharan, 2005 • Those who trust do not necessarily reciprocate. • Define a subject as “trusting” if he or she sent exactly 50% or more of her initial endowment of $10.00; otherwise “non-trusting” • Using the 50% cut-off we get 58 subjects who are non-trusting (sent less than 50%) and 42 trusting (sent exactly 50% or more). • The non-trusting subjects returned on average 18% of the amount they received while the trusting subjects returned 16%. • This difference is not significant using either a t-test or a Mann Whitney test and the result does not change when we try alternative definitions of “trusting”.

49. Chaudhuri and Gangadharan, 2005 • How about those who do reciprocate trust? Are they more trusting? • The answer turns out to be an emphatic yes. • Define “trustworthy” those who return at least 1/3 or more of any amount offered to them; otherwise “non trustworthy” • It turns out that the 27 trustworthy subjects send $5.33 on average which is higher than the $3.82 on average sent by the remaining 55 subjects. • (t = 1.79, p = 0.07 using a t-test and z = 1.84, p = 0.06 using a Mann Whitney test).

50. Chaudhuri and Gangadharan, 2005 • We next compare the behavior of the trustworthy receivers defined as those who send back 1/3 or more of the money received from the sender) and the less trustworthy ones (i.e. those who send back less than 1/3) in the dictator game. • We find that on average trustworthy subjects send $1.89 as the allocator in the dictator game. The less trustworthy ones send $0.83. • This difference is highly significant using a t-test (t = 2.251, p = 0.03) and marginally significant using the non-parametric Mann-Whitney test (z = 1.756, p = 0.08).