Reinhard Selten

End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach

Abstract A learning theory is proposed which models the influence of experience on end behavior in finite Prisoners Dilemma supergames. The theory is compared with experimental results. In the experiment 35 subjects participated in 25 Prisoners Dilemma supergames of ten periods each against anonymous opponents, changing from supergame to supergame. The typical behavior of experienced subjects involves cooperation until shortly before the end of the supergame. The theory explains shifts in the intended deviation period. On the basis of parameter estimates for each subject derived from the first 20 supergames, successful predictions could be obtained for the last five supergames.

A note on evolutionarily stable strategies in asymmetric animal conflicts

It is shown that in game models of asymmetric animal conflicts where the opponents assume different roles like “owner” and “intruder,” evolutionarily stable strategies must be pure strategies if a condition of information asymmetry holds. The condition is satisfied if two opponents always have different roles. Information about the opponents role may be incomplete.

An experimental solidarity game

Abstract 120 subjects played a three-person-game in which each player could win DM 10,00 with probability 2/3. Before the independent random decisions were made, the players had to decide under double blind conditions how much they were willing to give to one loser or each of two losers in the case of their winning. The great majority of subjects were willing to make substantial conditional gifts. The most common type of gift behavior does not lend itself to a straightforward interpretation as the result of altruistic utility maximization. We found an education effect, a gender effect, and a false consensus effect.

A simple model of imperfect competition, where 4 are few and 6 are many

The theory presented in this paper investigates the connection between the number of competitors and the tendency to cooperate within the context of a symmetric Cournot model with linear cost and demand, supplemented by specific institutional assumptions about the possibilities of cooperation. Cooperative forms of behavior are modelled as moves in a non-cooperative game. The proposition that few suppliers will maximize their joint profits whereas many suppliers are likely to behave non-cooperatively does not appear as an assumption but as a conclusion of the theory. For the simple model analyzed in this paper a definite answer can be given to the question where a “small group” of competitors ends and a “large group” begins: 5 is the dividing line between “few” and “many”.

Axiomatic Characterization of the Quadratic Scoring Rule

In the evaluation of experiments often the problem arises of how to compare the predictive success of competing probabilistic theories. The quadratic scoring rule can be used for this purpose. Originally, this rule was proposed as an incentive compatible elicitation method for probabilistic expert judgments. It is shown that up to a positive linear transformation, the quadratic scoring rule is characterized by four desirable properties.

Evolution, Learning, and Economic Behavior*

Abstract This is the entire text of the 1989 Nancy L. Schwartz Lecture delivered by the author at the J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois.

Features of experimentally observed bounded rationality

On the basis of experimental evidence reported in the literature the paper draws conclusions about the bounded rationality exhibited by human economic behaviour. Among the topics discussed are presentation effects caused by superficial analysis, strategic reasoning and strategy construction based on reciprocity and fairness, avoidance of circular concepts in step by step strategic reasoning, ex-post rationality and learning direction theory, presence of both adaptive and analytic approaches to repeated decision tasks, and the absence of quantitative expectations and optimization in typical repeated game strategies

Evolutionary stability in extensive two-person games

Abstract The concept of an ESS (evolutionary stable strategy) has been introduced by Maynard Smith and Price for two-person games in normal form (Maynard Smith and Price, 1973). The generalization to extensive two-person games raises various conceptual and mathematical problems, like the notion of symmetry in such games. A direct translation of the normal form concept to the framework of extensive games leads to unsatisfactory consequences. Therefore, on the basis of the trembling hand approach to perfectness (Selten, 1975), the notion of a limit ESS is introduced. Several theorems on the properties of a limit ESS provide tools for the analysis of specific games. Finally, a many-period model of animal contests with ritual fights and escalated conflicts is investigated in detail.

A Noncooperative Model of Characteristic-Function Bargaining

Cooperative game theory has produced quite a number of solution concepts for games in characteristic-function form. Among the most important theories are the von Neumann-Morgenstern solution (von Neumann-Morgenstern, 1944), the Shapley-value (Shapley, 1953), the bargaining set (Aumann-Maschler, 1964), and the nucleolus (Schmeidler, 1969). The aim of these and many other solution concepts has been normative, rather than descriptive, even if some primarily descriptive theories like equal-share analysis have been proposed (Selten, 1972).

Game theory and evolutionary biology

Publisher Summary The subject matter of evolutionary game theory is the analysis of conflict and cooperation in animals and plants. Originally, game theory was developed as a theory of human strategic behavior based on an idealized picture of rational decision making. Evolutionary game theory does not rely on rationality assumptions but on the idea that the Darwinian process of natural selection drives organisms toward the optimization of reproductive success. Most of evolutionary game theory focuses on those cases where stable equilibrium is reached. However, the dynamics of evolutionary processes in disequilibrium is also an active area of research. In principle, evolutionary game theory deals only with fully symmetric games. Asymmetric conflicts are embedded in symmetric games where each player has the same chance to be on each side of the conflict. The mathematical definition of evolutionary stability refers to symmetric games only. Because asymmetric conflicts can be embedded in symmetric games, this is no obstacle for the treatment of asymmetric conflicts.