The Ultimatum Game

The Ultimatum Game

2.1 The Ultimatum Game

The ultimatum game is a scenario in which two players must decide how to split a sum of money. The proposer makes an offer, and the responder can either accept or reject it. If the responder accepts, the money is split as proposed. If the responder rejects, both players receive nothing.

Examples of Ultimatum game behavior are as follows:

• Major League Baseball strike of 1994: Players rejected a revenue-sharing plan, forgoing $230$ million in salaries.

• Tokyo Kohtetsu Company takeover in 2007: Shareholders blocked a merger due to an unfair offer.

• Colin Camerer's cruise story: A photographer refused to negotiate the price of a photo, leading to no sale.

The Ultimatum Game Experiment

• Origin: Devised by Werner Güth, Rolf Schmittberger, and Bernd Schwarze in the early 1980s.

• Objective: To study bargaining behavior and responses to ultimatum offers.

• Method: 42 graduate students were paired, with one as the “proposer” and the other as the “responder.”

• Procedure: Proposers were given between 4 and 10 marks and had to suggest a split with the responder. The responder could accept, leading to the proposed split, or reject, resulting in both players receiving nothing.

Experimental Setup

• Proposers and responders were seated at opposite ends of a room, ensuring anonymity.

• Proposers had varying amounts of money (4 to 10 marks) to divide.

• The responder's decision was crucial: acceptance meant the proposed split, rejection meant both received nothing.

Economist's Perspective

• Backward Induction: Economists analyze such games using backward induction, starting from the responder's decision.

• Responder's Rationality: A rational responder should accept any non-zero offer, as something is better than nothing.

• Proposer's Strategy: Anticipating this, a proposer should offer the smallest possible amount.

• Nash Equilibrium: The predicted outcome is a minimal offer accepted by the responder.

Results of Güth's Experiment

• Unexpected Generosity: Proposers offered much more than the minimal amount, with one-third offering a 50-50 split.

• Rejection of Low Offers: Some responders rejected offers, even when they were non-zero.

• First Experiment: Seven out of 21 proposers offered exactly half (50%) of the initial amount. Seventeen out of 21 proposers (slightly more than 80%) offered the responder at least 20% or more of the total amount available. Two of the 21 offers were rejected

• Second Experiment: There were fewer 50-50 splits offered by the proposers (three out of 21, or 14%, as opposed to seven out of 21, or 33%, a week before). Eighteen out of 21 proposers (close to 86% and almost the same number as a week before) offered at least 20% of the available amount to the responder. Six of the 21 offers are rejected. In a number of cases, where the proposer wished to keep 80% or more of the available amount and offered the responder 20% or less, the responders turned down the offer.

Follow-Up Study

• Participants made two decisions: how much to offer as a proposer and the minimum acceptable amount as a responder.

• Most participants were consistent, offering what they would accept.

• Some recognized the proposer's advantage but were reluctant to exploit it fully.

Conclusions From Guth Experiments

• Decisions were driven by fairness notions rather than a misunderstanding of the game.

• Subjects reasoned, proposers make allowance for the fact that an offer may get turned down if it appears unfair to the responder, even if it gives the responder a relatively large payoff in absolute terms.."

• The results challenged the assumption of homo economicus, highlighting the importance of normative outcomes and relative payoffs.

2.2 Intentions, as well as outcomes, matter

Protesting Unfair Acts vs. Outcomes

• A key question: Are responders protesting the unfairness of the offer or the inequitable outcome?

• People may tolerate unfair outcomes resulting from chance factors more than deliberate acts.

Blount's Experiment

• Objective: To examine aversion to unfair acts versus protesting unfair outcomes.

• Conditions:

  • Usual ultimatum game.

  • “Third party” treatment: allocation decided by a disinterested participant.

  • “Chance” treatment: allocation decided by a roulette wheel.

Blount's Findings

• People were more willing to accept inequitable allocations when determined by chance.

• Intentional acts of unfairness led to lower minimum acceptable amounts.

• Minimum Acceptable Amounts: Responders were willing to accept more inequitable allocations when the division was decided by chance ($1.20) than by a third party ($2.08) or the proposer ($2.91). Seven out of 17 proposers offered a 50-50 split to the responder, four offered between$4 and $4.50, two offered between$2.50 and $3 and two offered the responder only$0.50.
  People were much less willing to accept large disparities in the payoffs in the condition where the proposer, who had a vested interest in the outcome, decided on the allocation, compared to the participants in the condition where the allocation was decided by chance.

Falk, Fehr, and Fischbacher's Experiment

• Objective: To provide evidence that intentions matter.

• Method: Participants played modified ultimatum games with restricted choices.

• Design: Proposers chose between offers A and B. Offer A was always 8 points for the proposer and 2 for the responder. Offer B varied across games.

  • 5/5 game: Offer B was 5 points for each.

  • 2/8 game: Offer B was 2 points for the proposer and 8 for the responder.

  • 10/0 game: Offer B was 10 points for the proposer and 0 for the responder.

• Results: The rejection rate of the 8/2 offer varied depending on the fairness of the alternative.

  • 5/5 game: 44.4% rejection rate.

  • 2/8 game: 27% rejection rate.

  • 10/0 game: 2% rejection rate.

Key Takeaway

Intentions driven reciprocal behavior is a major factor. If they are only concerned with their monetary payoffs then we expect that the 8/2 offer will never be rejected. In the "5/5 game" a proposal of 8/2 is clearly perceived as unfair In the "2/8 game" offering 8/2 may still be perceived as unfair but probably less so than in the "5/5 Finally, offering 8/2 in the "10/0 game" may even be perceived as a fair (or less unfair) action so that the rejection rate of 8/2 is likely to be lowest in this game.

Chimpanzee Behavior

• Jensen, Call, and Tomasello conducted a similar study with chimpanzees using raisins.

• Chimpanzees did not reject unfair offers when a fair offer was possible, unlike humans.

2.3 Criticisms of the findings of Güth and his colleagues

Sociability and Cooperation

Critics suggest that people are conditioned to be sociable and cooperative.

Ambiguous Situation

Assignment to roles is purely a matter of chance, which might make proposers feel less entitled to the money and more inclined to share it fairly with the responders.

Small Stakes

Critics argued that ten marks was not a large amount and therefore the participants may not even have taken the game seriously.

Experimenter Demand Effects

This suggests that even if a proposer is interested in pocketing most of the amount given to him, he may not do so because he knows that the experimenter can see his decisions and he does not want the experimenter to think of him as greedy.

2.4 Behaviour in the ultimatum game: fairness or altruism?

The Dictator Game

• Setup: Similar to the ultimatum game, but the responder has no say.

• Prediction: Proposer should take all the money.

• Comparison: Comparing offers in the ultimatum and dictator games reveals proposer motivations.

Forsythe, Horowitz, Savin and Sefton Experiment

• Results: Proposers in the ultimatum game offered more than in the dictator game.

• Conclusion: Proposers are motivated by fear of rejection rather than pure altruism.
  75% of proposers in the ultimatum game offered $2.00 or more (40$5.00, just about 70% of the proposers in the dictator game offered a dollar or less (20% or less).

2.5 Raising the monetary stakes in the ultimatum game

Hoffman, McCabe and Vernon Smith experiment

• They used $10 and$100, with roles assigned randomly or based on trivia quiz performance.

• Offers were similar in the $10 and$100 games when roles were random.

• “Earned” roles led to more parsimonious offers but higher rejection rates, especially in the $100 game.</p></li></ul><h5 id="a79cef7e-fa28-4ce7-ae41-2e8e206b8c02" data-toc-id="a79cef7e-fa28-4ce7-ae41-2e8e206b8c02" collapsed="false" seolevelmigrated="true">Lisa Cameron's Experiment</h5><ul><li><p><strong>Location</strong>: Gadjah Mada University in Yogyakarta, Indonesia.</p></li><li><p><strong>Stakes</strong>: 5,000, 40,000 and 200,000 Indonesian rupiahs (approximately$2.50, $20 and$100).

• Findings: Proposer behavior remained invariant to stake changes.

Average amount offered is around 40% in all three cases, and the modal amount is 50% in each case. In the game with 200,000 rupiahs, offers of 10% and 20% of the available amount were rejected by the responders. Offers does not become more parsimonious if it contains large sums of money.

2.6 Fear of punishment or fear of embarrassment?

The fear of punishment rather than fear of embarrassment is what leads to generous offers.

Hoffman, McCabe, Shachat and Vernon Smith

• Method: Ran dictator game experiments using a complicated “double-blind” protocol.

• Findings: Being observed by the experimenter - and possibly thought “greedy - seemed to matter, and that it is conceivable that it is this fear of being thought greedy that leads to generous offers in the ultimatum game rather than allowances for implicit social norms of fairness or the fear of being punished for unfair offers.

Gary Bolton and Rami Zwick

To provide an answer to this question and demonstrated beyond doubt that it was the fear of punishment that was driving behaviour in the ultimatum game

• Impunity Game: A rejection by the responder does not have the power to hurt the proposer by taking money away from him.

• Bolton and Zwick Comparison: Compared the behavior of participants in the ultimatum game with that in the impunity game

• Results: Found it was the fear of punishment was the primary motivation behind proposer choices.

2.7 Do norms of fairness differ across cultures?

Roth and his colleagues

Found by recruiting university students across four different locations - Pittsburgh, Ljubljana (in Slovenia which used to be part of Yugoslavia), Tokyo (in Japan) and Jerusalem (in Israel) that the prevailing norm as to what constitutes a fair offer influences behaviour in the ultimatum game.

• This study poses a number of ancillary problems.

  • Language effects

  • Experimenter effects.

Offers in the US and Slovenia were equally generous, while the offers in these two countries were more generous than the offers in Japan which in turn was more generous than the offers in Israel.

An even more ambitious cross-cultural study

• Joseph Henrich: An anthropologist at the University of California-Los Angeles (UCLA) was undertaking field work among the Machiguenga, a group of horticulturalists in the tropical forests of south-eastern Peru.

• Results: The Machiguenga behaved very differently from the participants in the studies mentioned above. The most common offer made by Machiguenga proposers was 15% and despite many low offers, not a single offer was rejected.

Broad Overview of Behaviour in the Ultimatum Game

• Offers Across Diverse Societies: From Machiguenga proposers was 15% to others from Achuar and the Orma provide a little more than 40% of the pie.

The large variations across the different cultural groups suggest that preferences or expectations are affected by group-specific conditions, such as social institutions or cultural fairness norms.

The important question is the payoff to cooperation i.e. how important and how large is a group's payoff from cooperating in day-to-day economic production.

2.9 What does a preference for fairness have to do with economics?

Fairness as a constraint on profit-making

• Daniel Kahneman, a psychologist at Princeton, and two economists Jack Knetsch of Simon Fraser University and Richard Thaler of Cornell in the mid-1980s.

Exploitation of increased market power

By and large that such price-gouging is unfair because such an action would constitute opportunistic behaviour.

The context for pricing decisions

These increases were considered acceptable by 79% and 75% of the respondents, respectively. This suggests that it is acceptable for firms to protect themselves from losses even if this means raising prices.

Enforcement

Sixty-eight per cent of respondents in this survey said they would switch their patronage to a drugstore five minutes further away if the one closer to them raised its prices when a competitor was temporarily forced to close; and, in a separate sample, 69% indicated they would switch if the more convenient store discriminated against its older workers.

Fairness in labour markets

Findings of the study by Kahneman and his colleagues suggest that many actions that are both profitable in the short run and not obviously dishonest are likely to be perceived as unfair exploitations of market power.

Economic consequences

Bradley Ruffle, of Ben Gurion University in Israel, decided to set up an experiment to test if buyers do indeed refrain from buying at prices they consider to be unfair.

What Ruffle finds is that indeed “demand withholding” by buyers - where the buyers essentially refuse to buy at prices which gives most of the surplus to the sellers is a factor in these markets.

2.10 Concluding remarks

People are willing to turn down a deal offering substantial monetary amounts if they believe that they are being treated unfairly.

However, a recent study by Gary Bolton, Jordi Brandts and Axel Ockenfels suggests that at times a fair procedure can be a substitute of a fair outcome. In their study proposers in an ultimatum game have three choices initially