The Ultimatum Game

1. The Ultimatum Game

2. Powerpoint based on the following articles • Bowles and Gintis: 15 small scale societies • Camerer and Thaler: Ultimatums, Dictators and Manners • Camerer: When does “Economic Man” Dominate in Social Behavior? • Kahneman, Knetsch and Thaler: “Fairness and the Assumptions of Economics”

3. The Ultimatum Game Güth, W., Schmittberger, and Schwarze (1982). "An Experimental Analysis of Ultimatum Bargaining". Journal of Economic Behavior and Organization: 367–388. The proposer makes a single offer to a responder about how to split some amount of money (e.g., $10 in $1 units). The responder must either i) accept the proposed split or ii) reject the proposal, which results in zero earnings for both parties.

4. Ultimatum game: Standard Prediction Proposer Goal: solve for proposer’s equilibrium offer xStart at the bottom 0 10 x What will Responder accept? Responder Offer of 1, 2, … 10, but not 0 Accept Reject 10-x, x 0, 0

5. Ultimatum game: Standard Prediction Proposer If proposer offers 1 will responder accept? 0 10 Yes, 1 is better than zero 1 Does proposer have an incentive to deviate from this strategy? Could he do better by offering 2? Responder Accept Reject No, while responder earnings rise to 2, the proposer does not need to make this offer to induce acceptance and with earnings of 8 the proposer is worse off. 9, 1 0, 0

6. Ultimatum game: Standard Prediction Proposer 0 10 X = 1 is a Nash equilibrium. It is not fair to the responder, but shows the advantage of being the one who calls the equilibrium. 1 Responder Accept Reject 9, 1 0, 0

7. Prediction of Standard Economic Theory A “rational” proposer would offer $1 and keep $9 for him/herself. A “rational” responder would accept $1, reasoning that $1 is better than nothing, and not crash the deal. Findings to the contrary suggest that people do no have purely self-regarding preferences

8. Class Experiment Treatment #1 – Dictator Game run by hand. $10 (10 x $1) given to a student chosen at random who is then invited to share some with neighbor. Treatment #2 – Dictator Game run in Veconlab . Treatment #3 – Ultimatum Game run in Veconlab . I will pay two students, chosen at random, 1/0 of their cumulative earnings after 12 rounds of Treatments 1 and 2 run in Veconlab.

9. Standard Empirical Findings • In Industrial cultures, irrespective of monetary sum, modal offers are around 50% of total amount. • Low offers (20%) have about a 50% chance of being rejected. Results contradict predictions of standard game theory.

10. First Explanation – Low Stakes • Is the phenomenon simply a function of the small stakes used in the lab? • Unequal allocations are rejected only because the absolute amount of the offer is low. If the amount to be split were ten million dollars a 90:10, the split would probably be accepted rather than spurning a million dollar offer.

11. Literature on Stakes • Cameron and Hoffman et al. (1994) – the higher the stakes the closer offers approach an even split, even in a 100 USD game played in Indonesia, where average 1995 per-capita income was 670 USD. Rejections are reportedly independent of the stakes at this level, with 30 USD offers being turned down in Indonesia, as in the US, even though this equates to two week's wages in Indonesia.

12. More on Stakes • Hoffman, McCabe and Smith – invested $5,000 in research funds to find out what would happen. They had 50 pairs play $100 version of an UG in two conditions • Random proposer • Framed proposer Compared results to earlier game with $10 stakes Results? No differences in means

13. Second Explanation Bolton (1991) - Utility includes social comparison + + U(xR, xR/xP) xR = absolute earnings received by responder xR/xP = ratio of responder’s earning to proposer’s earning (1 if both get zero) Example: Responder rejects $2 out of $10 offer U($2, 0.25) < U($0, 1)

14. Problem with Second Explanation? Social comparison theory does not distinguish between: a) distaste for unequal allocations b) willingness to punish someone who has behaved “unfairly” Blount (1996): Subjects are more likely to accept small (uneven) offers it they come from a random device than from a person Conclusion: People are punishing unfairness, not rejecting inequality

15. Sanfey, et al. Science (2003).

16. Third Explanation: Intentions Matter Mathew Rabin (1993) Intentional acts of meanness Punish Unintentional acts of meanness Tolerate Fairness equilibrium - both parties will sacrifice to reward (punish) other player’s cooperative (uncooperative) act

17. Push-Pull Game: Prisoner’s Dilemma Fairness Equilibrium (both parties willing to sacrifice to reward other player’s cooperative act) Column Player Cooperate Defect 3 3 5 0 Cooperate Row Player 5 0 2 2 Defect Fairness Equilibrium (both parties punish uncooperative behavior of others) Nash Equilibrium

18. Implications If intentions matter we can explain… 1) Difference in results from ultimatum game when played with computer 2) Simultaneous,… Positive altruism (helping friends with gifts or trust) Negative altruism (punishing enemies at a cost to oneself)

19. Camerer and Thaler (1996) Rabin has it right - Manners Matter Findings: People share in dictator games, but sharing shrinks when a) the relationship with the other player is made less personal or 2) when proposer “earned” the right to the $10. Conclusion: “Manners” require you to share a windfall with a friend, do not require that you give up a hard-earned bonus to a stranger.” Findings: Responders reject low (but greater than $1) offers. Conclusion: Responders in ultimatum game are willing to turn down rude offers at a cost to themselves.

20. More Evidence for Rabin’s “Manners Matter” Finding: When Responders must compete with one another to take an offer from single Proposer, minimal acceptable offers fell to 10% (Roth et al. 1991). Conclusion: Individual Responders don’t have the ability to single-handedly punish unfair offers. Since the Proposer is not suggesting an offer in these games – he is taking the best offer from competing Responders – the prospect of unfair offers is removed. These findings are consistent with idea that manners about fairness norms matter.

21. Is a sense of fairness learned? Murnighan and Saxon (1994) Kindergartners accept minimal offers (e.g., one M&M out of a pile) about 70% of the time 3rd and 6th graders accept minimal offers about 40% of the time learned behavior

22. Is a sense of fairness genetic? Wallace, Cesarini, Lichtenstein and Johannesson, “Heritability of Ultimatum Game Responder Behavior” Proceedings of the National Academy of Sciences, October 2007. Abstract: Experimental evidence suggests that many people are willing to deviate from materially maximizing strategies to punish unfair behavior. Even though little is known about the origins of such fairness preferences, it has been suggested that they have deep evolutionary roots and that they are crucial for maintaining and understanding cooperation among non-kin. Here we report the results of an ultimatum game, played for real monetary stakes, using twins recruited from the population-based Swedish Twin Registry as our subject pool. Employing standard structural equation modeling techniques, we estimate that >40% of the variation in subjects' rejection behavior is explained by additive genetic effects. Our estimates also suggest a very modest role for common environment as a source of phenotypic variation. Based on these findings, we argue that any attempt to explain observed ultimatum bargaining game behavior that ignores this genetic influence is incomplete.

23. Identical Twins (share all genes) Fraternal Twins (share 50% of genes) Fig. 2. Scatter plot of ultimatum game acceptance thresholds for twin pairs. (A) Scatter plot for MZ twin pairs. The acceptance thresholds are highly correlated. (B) Scatter plot for DZ twin pairs. There was no significant correlation in acceptance thresholds.

24. Sanfey, et al. Science (2000) What is the evolutionary explanation for this behavior? A fundamental adaptive mechanism by which we assert and maintain a social reputation. Unfair treatment causes people to sacrifice monetary gain to punish partners for slight.

25. Sanfey, et al. Science (2003) Subjects whose brains were scanned by MRI while receiving an unfair offer in an ultimatum game ($1 or $2 out of $10 available) showed greater activity in the bilateral anterior insula of the brain. The anterior cingulate (ACC), a region of the brain that detects cognitive conflict, also showed greater activity during presentation of unfair offers. This area mediates conflict between earning money and feeling bad. Overall, work emphasizes importance of emotional influences on human decision making.

26. Neuroeconomics

27. What about Chimpanzees? Jensen, Call and Tomasello, “Chimpanzees Are Rational Maximizers in an Ultimatum Game,” Science Magazine, 2007. Abstract: Traditional models of economic decision-making assume that people are self-interested rational maximizers. Empirical research has demonstrated, however, that people will take into account the interests of others and are sensitive to norms of cooperation and fairness. In one of the most robust tests of this finding, the ultimatum game, individuals will reject a proposed division of a monetary windfall, at a cost to themselves, if they perceive it as unfair. Here we show that in an ultimatum game, humans' closest living relatives, chimpanzees (Pan troglodytes), are rational maximizers and are not sensitive to fairness. These results support the hypothesis that other-regarding preferences and aversion to inequitable outcomes, which play key roles in human social organization, distinguish us from our closest living relatives.

28. Fig. 1. Illustration of the testing environment. The proposer, who makes the first choice, sits to the responder's left. The apparatus, which has two sliding trays connected by a single rope, is outside of the cages. (A) By first sliding a Plexiglas panel (not shown) to access one rope end and by then pulling it, the proposer draws one of the baited trays halfway toward the two subjects. (B) The responder can then pull the attached rod, now within reach, to bring the proposed food tray to the cage mesh so that (C) both subjects can eat from their respective food dishes (clearly separated by a translucent divider)

29. Camerer and Thaler Conclusion In repeated encounters, it is rational to treat others fairly and punish those who behave unfairly, because long-run concerns outweigh the short-run costs How do we explain behavior in one-shot games (e.g., tips in restaurants) People cannot curb their repeated –game impulse

30. Effect of Competition? (Camerer: when does economic man dominate?)

31. More

32. Discussion • A minority of self-regarding individuals can trigger a “non-cooperative” aggregate outcomes. • A minority of other-regarding individuals can generate a “cooperative” aggregate outcome.

33. In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies • Bowles and Ginits project to uncover the following questions: • Are the deviations from the canonical model evidence of universal patterns of behavior or do the individual’s economic and social environment shape behavior? • Which economic and social conditions are involved?

34. Bowles and Gintis Questions • Is reciprocal behavior better explained statistically by individuals’ attributes such as their sex, age, or relative wealth or • By the attributes of the group to which the individual belongs? • Are there cultures that approximate the canonical account of self-regarding behavior?

35. How to address questions? • Cross-cultural study of behavior in ultimatum, public good, and dictator games • 12 researchers, 12 countries, 5 continents, 15 small-scale societies

36. Types of Societies • Three foraging societies • Six that practice slash-and-burn horticulture • Four nomadic herding groups • Three sedentary, small-scale agricultural societies.

37. Results • 1. the canonical model is not supported in any society studied • 2. there is considerably more behavioral variability across groups than had been found in previous cross-cultural research, and the canonical model fails in a wider variety of ways • 3. group-level differences in economic organization and the degree of market integration explain a substantial portion of the behavioral variation across societies

38. Specific Results • The higher the degree of market integration and the higher the payoffs to cooperation, the greater the level of cooperation in experimental games • 4. individual-level economic and demographic variables do not explain behavior either within or across groups • 5. behavior in the experiments is generally consistent with economic patterns of everyday life in these societies.

39. Their experiment • “Proposer” gets an amount equivalent to a day or two’s wages in the society and asked to propose an offer to a secondary person, the “respondent” • Respondent can either accept or reject • Game is mostly played anonymously

41. Discussion of Results • Even the groups with the smallest offers have mean offers great than 25% of stake size • Large variation in mean offers across societies • Torguud and Mapuche: offered between 30 percent and 40 percent • Achuar and Sangu: between 40 percent and 50 percent • Ache and the Lamerlara: mean offers greater than 50%

42. Comparing Means • These group differences are strikingly large compared to previous cross-cultural work comparing ultimatum game behavior among university students (Roth et al 1991) • Industrial Society Means: 44% • Industrial Society Modes: 50% • Mean in our sample: 26% to 58% • Modes in our sample: 15% to 50%

43. Comparing Rejections • Rejection rates are also much more variable: • Industrial societies offers below 20% are rejected with probability of 0.4 to 0.6 • Rejections of low offers are extremely rare among some groups • In other groups substantial and frequent rejections to even offers above 50%!

44. How to Analyze Data? • Rank-ordered societies along two dimensions: • 1. Payoffs to Cooperation (PC): How important and how large is a group’s payoff from cooperation in economic production? • With little cooperative production, there will be little necessity to share returns. High PC should lead to increased sharing behavior in UG. • 2. Market Integration (MI): How much do people rely on market exchange in their daily lives? • The more frequently people experience market transactions, the more they will also experience abstract sharing principles concerning behaviors toward strangers of which the UC is an example

45. Example and discussion • Machiguenga and Tsimane: rank lowest in PC. They are almost entirely economically independent at the family level and engage rarely in productive activities involving more than members of a family. • Lamelara whale hunters: go to sea in large canoes manned by a dozen or more individuals.

46. Explain group mean UG offers on basis of those dimensions • Regression analysis: both PC and MI were highly significant. • Explanation: when faced with a novel situation like the UG game, people looked for analogues in their daily experience. • Hyper-fair offers and frequent rejections of the Au and Gnau reflect the culture of gift giving.

47. More Examples • In New Guinea, accepting gifts, even unsolicited ones, commits one to reciprocate at some future time to be determined by the giver. • Receipt of large gifts also establishes one in a subordinate position. • Consequently, large gifts are often refused

48. The Ache • Did not reject low offers, and despite this the vast majority of the Ache (94%) made offers above 40% of the stake size. This coincides neatly with ethnographic descriptions indicating widespread meat-sharing and cooperation in community projects despite the absence of a fear of punishment in society.

49. Ache Continued • Ache hunters, returning home, quietly leave their kill at the edge of camp, often claiming that the hunt was fruitless; their catch is later discovered and collected by others and then meticulously shared among all in the camp.

50. The Machiguenga & the Orma • Lowest cooperation rates in public-goods games, reflecting ethnographic descriptions of Machiguenga life: • Little cooperation, exchange or sharing beyond the family. • Orma, called the public-goods game “harambee” referring to the widespread institution of village-level voluntary contributions for public-goods projects (they contributed 58%)