4. Extensive- form games. The Ultimatum Game. Güth, W., Schmittberger, and Schwarze (1982). "An Experimental Analysis of Ultimatum Bargaining". Journal of Economic Behavior and Organization : 367–388.
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.
Goal: solve for proposer’s equilibrium offer xStart at the bottom
What will Responder accept?
Offer of 1, 2, … 10, but not 0
If proposer offers 1 will responder accept?
Yes, 1 is better than zero
Does proposer have an incentive to deviate from this strategy? Could he do better by offering 2?
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.
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.
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
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.
Results contradict predictions of standard game theory.
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.
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.
Bolton (1991) - Utility includes social comparison
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)
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
Mathew Rabin (1993)
Intentional acts of meanness
Unintentional acts of meanness
Fairness equilibrium - both parties will sacrifice to reward (punish) other player’s cooperative (uncooperative) act
Fairness Equilibrium (both parties willing to sacrifice to reward other player’s cooperative act)
Fairness Equilibrium (both parties punish uncooperative behavior of others)
If intentions matter we can explain…
1) Difference in results from ultimatum game when played with computer
Positive altruism (helping friends with gifts or trust)
Negative altruism (punishing enemies at a cost to oneself)
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: “Manors” 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.
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.
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
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.
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.
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.
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.
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.
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)
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