Ultimatum game
The ultimatum game is one of the practical applications of game theory for economic and behavioral research. It was developed by Güth et. al. (1982) implemented experimentally. The ultimatum game is often used as a laboratory experiment to investigate the altruism or selfishness. In different variations of the game is investigated to what extent the person maximizes only the results from the in-game item benefits and the extent to which the person also involves other interests in his decisions. Examples to consider other interests are the maintenance of rules that use it, or the community, and cultural practices such as the sense of justice, as well as the work of one's own personality image on other players and observers. Also for neurobiological experiments is the ultimatum game - among others - successfully used to investigate, for example, the effects of ( damaged ) areas of the brain on behavior. A multiplayer version is the so-called Pirate game.
Basic form of the ultimatum game
An actor A1 is provided a good (eg, money). Of this he has to choose a part ( ) and another actor A2 offer. Rejects this the part offered to him from, it must also A1 renounce his part and both get nothing. If A2, so he receives the offer and A1 receives the rest.
One goal of the game is for the player A1 is to maximize its profits in the form of money. ( He could, however, have other goals, for example, the money "fairly" divide. In the present observation profit maximization is assumed. ) Player A2 The goal is the player A1 is not necessarily known. It can be assumed on the basis of social experience it though. In the standard version of the ultimatum game, the players are not known and can not communicate with each other. Thus the two players have no consequences to fear except for a non- profit.
The game theoretic solution for profit-oriented rational players is that A1 of the sum of only the lowest part (eg " 1 Cent " ) offers because he knows that in terms of individual utility maximizing rational player A2 prefer this small amount of a payment of zero and is therefore agree (with a payoff of zero would result for A2 no advantage, so he could refuse ). A1 has thus minimizing its investment and the amount paid out to him even share maximized. In experiments, however, many players A2 behaved in this sense rationally, but rather rejected a small profit from, to accept it as a perceived unfair allocation. Offers below about 15 % of the total are usually rejected, so that the seller gets nothing. The distribution is slightly different. On average, about 30% of the goods can be A1 A2. Common is practically always a distribution which drastically differs from the "rational " division.
Is A1 already owner of the estate, and it may leave a part of A2, where as before A1 additionally receives as a positive, there are three interesting solutions:
If the good is of A1 in this case greater than that of A2, then the third solution, based on the absolute profit, detrimental to A2. Only when the estate of A2 is larger than that of A1, A2 is the solution for 3 advantage - and vice versa: The one who has more good, will try to enforce solution 3, the other will go for the solution 2. If the good is of A1 and A2 equal, the solutions 2 and 3 are identical.
Is that your own good than of the game partner, so it is advantageous to hide his own good as much as possible towards the game partners to increase the probability of realization of the solution 2. In contrast, it is important for the richer game partners to identify the entire estate of the poorer game partner, so as not to arouse the suspicion of unfairness in the attempt to enforce the solution 3. Here, the measure of fairness is culturally dependent.
If an allocation is made under more than one, then increases the willingness to accept smaller sums.
The distribution is also partially dependent on the specific cultural practices.
In economics, a Pareto- optimal equilibrium refers to a distribution of scarce goods in which no party can be made better off without putting another worse.
Variant: dictator game
A dictator game is a variant of this game in the A2, the offer can not refuse. In this variant, one would expect only the smallest possible offer when a loss minimization in the domain of obvious utility function ( giving away as little money as possible) would be the only relevant behavior. If a loss mitigation ( "greed " ) in this area is not dominant observable, it must be examined ( for example, maintenance of cooperation for future games ) affect what other utility functions, the decisions of the participants in this game.
Utility maximization at various levels
Does not that individual rationality following behavior to maximize the benefits (eg, money, resources ) for a group, then played with collective rationality. If a game no utility maximization (or at least minimize losses ) to watch, then there is either no rationality or it was played by a not yet perceived benefits, for example in a metagame to future benefits locking rules. Ultimatum games are well suited to represent this situation and demonstrate paradoxification in the game analysis.
In ultimatum games and the difference between individual and often repeated games is clear. Here the single game is played in communities so that the current from individual games overall game maximizes the benefit of the community or minimize losses. This results in an efficient sharing and distribution of resources within this community may result.
Empirical results
Players from developed countries - mostly undergraduate students from the United States, Europe and Asia - have typically between 40 % and 50 % of the sum of the second player, and offers less than 30% are rejected by the second player in the rule. Martin A. Nowak et al. (2000) were able to predict these results in a model if this reputation into account, that tells information about the behavior of a player in the past. Nowak et al. concluded that the ultimatum game show a universal human tendency to fair and punishing behavior. Since the experiments are played without a reputation, but only the results are similar to those of simulations with reputation, went Nowak et al. assume that fairness and punishment out trained for in an evolutionary context in which interactions without reputation were not fitness relevant.
However, in other cultural contexts, the ultimatum game came to different results. Joseph Henrich et al. led through the game with several randomly selected small ethnic groups. It was found that players from the industrialized countries represented the high extreme of the range of offers and rejections. In the smallest companies were made very low bids and does not refused. Therefore, these results were similar to the simulations, Nowak et al. Before considered reputation. In the U.S., the dictator game, on average, almost twice (> 45 %) were made so high as deals with the Hadza (< 30%). The ultimatum game brought similar results, also is the rejection threshold higher in the U.S. than in any other studied society. The analysis of these data shows that the degree of market integration (percentage of calories consumed that were purchased ) and the degree of religiosity predict both independently of each other higher offers. In other words, the results of the ultimatum game in industrialized countries are not specifically attributable human universals, but on the cultural development of these societies. Henrich et al. assume that complex market-based societies, not without a high degree of cooperation with strangers are possible.