Games - Ultimatum game

Home > Listing Index > Games > Ultimatum game

	Games - Ultimatum game

The ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. The first player proposes how to divide a sum of money with the second party. If the second player rejects this division, neither gets anything. If the second accepts, the first gets their demand and the second gets the rest.

Equilibrium analysis

For illustration, we will suppose there is a smallest division of the good available (say 1 cent). Suppose that the total amount of money available is x.

The first player chooses some amount in the interval . The second player chooses some function f: -> {"accept", "reject"}. We will represent the strategy profile as (p, f), where p is the proposal and f is the function. If f(p) = "accept" the first receives p and the second x-p, otherwise both get zero. (p, f) is a Nash equilibrium of the Ultimatum game if f(p) = "accept" and there is no y > p such that f(y) = "accept". I.e. p is the largest amount the second will accept. The first player would not want to unilaterally increase their demand since the second will reject any higher demand. The second would not want to reject the demand, since he would then get nothing.

There is one other Nash equilibrium where p = x and f(y) = "reject" for all y>0 (i.e. the second rejects all demands that gives the first any amount at all). Here both players get nothing, but neither could get more by unilaterally changing their strategy.

However, only one of these Nash equilibria satisfies a more restrictive equilibrium concept subgame perfection. Suppose that the first demands a large amount that gives the second some (small) amount of money. By rejecting the demand, the second is choosing nothing rather than something. So, it would be better for the second to choose to accept any demand that gives him any amount whatsoever. If the first knows this, they will give the second the smallest (non-zero) amount possible.

Experimental results

In many cultures, people (except economics grad students) offer "fair" (e.g., 50:50) splits, and offers of less than 20% are often rejected (Henrich et al. 2004; Oosterbeek et al. 2004). These results (along with similar results in the Dictator Game) are taken to be evidence against the Homo economicus model of individual decisions. Since an individual who rejects a positive offer is choosing to get nothing rather than something, individuals must not be acting solely to maximize their economic gain. Several attempts to explain this behavior are available. Some authors suggest that individuals are maximizing their expected utility, but money does not translate directly into expected utility (Bolton 1991; Ochs and Roth 1989). Perhaps individuals get some psychological benefit from engaging in punishment or receive some psychological harm from accepting a low offer.

Based on fMRI studies of the brain during decision-making, different brain regions activate dependent upon whether the participating subject "accepts" or "declines" an offer. Since to "decline" means that neither receives any money, the responder is actually "punishing" the player who makes a low offer. Punishing activates the part of the brain that is associated with the dopamine pathway--e.g. it provides pleasure to punish. Hence, the subjects who refuse to accept and punish in the process, possibly receive more pleasure from punishment than they would from accepting a low offer. This is, therefore, an expected utility argument where the currency of "utils" is in pleasures received rather than goods or their associated values in money.

Explanations

The classical explanation of the Ultimatum game as a well-formed experiment approximating general behaviour often leads to a conclusion that the Homo economicus model of economic self-interest is incomplete. However, several competing models suggest ways to bring the cultural preferences of the players within the optimized utility function of the players in such a way as to preserve the utility maximizing agent as a feature of microeconomics. For example, researchers have found that Mongolian proposers tend to offer even splits despite knowing that very unequal splits are almost always accepted. Similar results from other small-scale societies players have led some researchers to conclude that “reputation” is seen as more important than any economic reward. Another way of integrating the conclusion with utility maximization is some form of Inequity aversion model (preference for fairness).

An explanation which was originally quite popular was the “learning” model, in which it was hypothesized that proposers’ offers would decay towards the sub game perfect NE (almost zero) as they mastered the strategy of the game. (This decay tends to be seen in other iterated games). However, this explanation (bounded rationality) is less commonly offered now, in light of empirical evidence against it.

[ Visit the complete Wikipedia entry for Ultimatum game ]

Searches on eBay

ultimatum game