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OLIGOPOLISTIC pricing decisions—in which the choice variable is not dichotomous as in the simple Prisoner’s Dilemma but continuous—have been modeled as a Generalized Prisoner’s Dilemma (GPD) by Fader and Hauser, who sought, in the two MIT Computer Strategy Tournaments, to obtain an effective generalization of Rapoport’s Tit for Tat for the threeperson repeated game. Holland’s genetic algorithm and Axelrod’s representation of contingent strategies provide a means of generating new strategies in the computer, through machine learning, without outside submissions. The paper discusses how findings from two-person tournaments can be extended to the GPD, in particular how the author’s winning strategy in the Second MIT Competitive Strategy Tournament could be bettered. The paper provides insight into how oligopolistic pricing competitors can successfully compete, and underlines the importance of “niche ” strategies, successful

It is assumed that players bundle nodes in which other players must move into analogy classes, and players only have expectations about the average behavior in every class. A solution concept is proposed for multi-stage games with perfect information: at every node players choose best-responses to their analogy-based expectations, and expectations are correct on average over those various nodes pooled together into the same analogy classes. The approach is applied to a variety of games. It is shown that a player may beneÞt from having a coarse analogy partitioning. And for simple analogy partitioning, (1) initial cooperation followed by an end opportunistic behavior may emerge in the Þnitely repeated prisoner’s dilemma (or in the centipede game), (2) an agreement need not be reached immediately in bargaining games with complete information.

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This paper presents a dynamic model in which agents adjust their decisions in the direction of higher payoffs, subject to random error. This process produces a probability distribution of players' decisions whose evolution over time is determined by the Fokker-Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studied games. In equilibrium, the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs. This "logit equilibrium" forms a stochastic generalization of the Nash equilibrium and provides a possible explanation of anomalous laboratory data.

The language of game theory—coalitions, payo¤s, markets, votes— suggests that it is not a branch of abstract mathematics; that it is motivated by and related to the world around us; and that it should be able to

The creation of mathematical, as well as qualitative (or rule-based), models is difficult, time-consuming, and expensive. Recent developments in evolutionary computation hold out the prospect that, for many problems of practical import, machine learning techniques can be used to discover useful models automatically. These prospects are particularly bright, we believe, for such automated discoveries in the context of game theory. This paper reports on a series of successful experiments in which we used a genetic programming regime to discover high-quality negotiation policies. The game-theoretic context in which we conducted these experiments --- a three-player coalitions game with sidepayments --- is considerably more complex and subtle than any reported in the literature on machine learning applied to game theory. 1. Introduction 1 Modeling is difficult, time-consuming, and expensive. Examining a real-world system, collecting data, and summarizing the findings in the form of a valid...

John Nash's formulation of noncooperative game theory was one of the great breakthroughs in the history of social science. Nash's work in this area is reviewed in its historical context, to better understand how the fundamental ideas of noncooperative game theory were developed and how they changed the course of economic theory.

1992 version is intended as a contribution to a two volume collection honouring Patrick Suppes, to be edited by Paul Humphreys and published by Kluwer Academic Publishers. ABSTRACT. In an extensive form game, whether a player has a better strategy than in a presumed equilibrium depends on the other players ’ equilibrium reactions to a counterfactual deviation. To allowconditioning on counterfactual events with prior probability zero, extended probabilities are proposed and given the four equivalent characterizations: (i) complete conditional probability sys-tems; (ii) lexicographic hierarchies of probabilities; (iii) extended logarithmic likelihood ratios; and (iv) certain ‘canonical rational probability functions ’ representing ‘trembles ’ directly as in-finitesimal probabilities. However, having joint probability distributions be uniquely determined by independent marginal probability distributions requires general probabilities taking values in a space no smaller than the non-Archimedean ordered field whose members are rational functions of a particular infinitesimal. Elinor now found the difference between the expectation of an unpleasant event, however certain the mind may be told to consider it, and certainty itself. — Jane Austen, Sense and Sensibility, ch. 48.... a more attractive and manageable theory may result from a non-Archimedean representation.... One must keep in mind the fact that the refutability of axioms depends both on their mathematical form and their empirical interpretation. — Krantz, Luce, Suppes and Tversky (1971, p. 29).

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