# Ultimatum Game

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The ultimatum game is a variation of game theory that has become popular in the field of experimental economics. The game involves players making sequential moves in a simple take-it-or-leave-it bargaining environment.

In the traditional ultimatum game experiment, two players are randomly and anonymously matched. One person, the proposer, receives a fixed amount of money and must offer a suggested split of this money with another person, the responder. The responder must accept or reject the offer as it is presented. They are told they will play the game exactly one time.

For example, assume Player 1, the proposer, receives $20 to split with Player 2, the responder. Figure 1 below illustrates the choices available to each player and payoff amounts associated with each choice. Player 1 may choose an even split, giving$10 to each person, or an uneven split, such as keeping $18 and offering$2. Player 2 may either accept or reject this offer.

If Player 1 offers an even split, and Player 2 accepts it, both receive $10. If Player 1 offers an uneven split that Player 2 accepts, then Player 1 gets$18 and Player 2 gets $2. If Player 2 rejects the offer, both players receive$0.

### Figure 1: Illustration of payoffs in an Ultimatum Game

Traditional economic theory suggests people are rational, self-interested, and seek to maximize their utility. In theory, proposers would offer the least amount of money they believe a responder would accept, while responders would accept any amount of money offered because a few dollars is better than nothing.

The results from ultimatum game experiments used in a variety of real-life settings, however, suggest the potential for responders to reject an â€śunfairâ€ť offer encourages proposers to propose more even splits of the money.

The degree of familiarity, or social distance, between two people may also affect their choices. When players come from a shared social group (e.g., a village or a class in school), offers tend to be more â€śfairâ€ť or evenly split. Additionally, responders often reject offers of 20% or less even though they experience a financial cost from this choice (Camerer, 2003; Oosterbeek, Sloof, and Van de Kuilen, 2003).

These results challenge the expectation that traditional economic theory would give us, as discussed above. The results do this by suggesting that receivers gain some value in signaling that unfair offers are unacceptable, and proposers likely account for the probability that an unfair offer is rejected when making their proposal.

Hoffman et al. (1996) examined ultimatum game behavior when participant roles were determined by a contest.

Before participating in the experiment, subjects took a current events quiz, and their scores were ranked. Higher scoring individuals became proposers who were matched with a lower-scoring responder. Results revealed proposers offered substantially less when they felt their roles were justified and legitimate compared to when roles were assigned randomly.

Additionally, responders tended to accept lower offers when they were splitting $10. When the amount of money to split was$100, however, rejection rates for lower offers increased significantly. The authors concluded responders were willing to accept the proposerâ€™s role as justifiable when the stakes are low, but they became less willing to accept the proposers earned their roles legitimately as the stakes increased.

## Good to Know

A modified version of the ultimatum game is the Dictator Game. In this experimental setting, one person (the dictator) receives an endowment and must decide how much of it to offer to an anonymous, random recipient. Unlike in the ultimatum game, however, the recipient must accept the amount offered and has no ability to punish the dictator if the offer is unacceptable.

Traditional economic theory suggests players acting as dictators would make offers of \$0 since there are no consequences. But, real-life experimental results suggest when the players are unknown to each other, dictatorsâ€™ offers are lower.

As with the findings from ultimatum game experiments, when there is less social distance between participants, dictators often allocate some money to the recipients, reducing the amount for themselves. This tendency to offer a non-zero share of the endowment indicates people may consider not only self-interest, but also ideas of fairness and altruism in their decision-making, especially in organizations. Less social distance between organizational members may encourage more prosocial behavior, improving the welfare of the organization and organizational outcomes.

Research on dictator game experiments suggests information about the recipient may affect how much a dictator offers, too. BraĂ±as-Garza (2006) examined dictator behavior in three different information conditions.

• First, when dictators received no information about recipients, 71% of dictators donated nothing. The average donation was 10% of the endowment.
• Second, when dictators were informed recipients were poor and from underdeveloped countries where this money could be useful, 46% of dictators donated the full endowment and 22% donated nothing.
• Third, when dictators were told the recipients were poor and that donations would be in medicines rather than money, 72% of dictators donated the full amount, and the average donation was 65% of the endowment.

The authors concluded that knowing recipients were poor encouraged more altruistic behavior from the dictators.

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