We use simple learning models to track the behavior observed in experiments concerning three extensive form games with similar perfect equilibria. In only two of the games does observed behavior approach the perfect equilibrium as players gain experience. We examine a family of learning models which possess some of the robust properties of learning noted in the psychology literature. The intermediate term predictions of these models track well the observed behavior in all three games, even though the models considered differ in their very long term predictions. We argue that for predicting observed behavior the intermediate term predictions of dynamic learning models may be even more important than their asymptotic properties.

Darwinian evolution is based on three fundamental principles, reproduction, mutation and selection, which describe how populations change over time and how new forms evolve out of old ones. There are numerous mathematical descriptions of the resulting evolutionary dynamics. In this paper, we show that apparently very different formulations are part of a single unified framework. At the center of this framework is the equivalence between the replicator–mutator equation and the Price equation. From these equations, we obtain as special cases adaptive dynamics, evolutionary game dynamics, the Lotka-Volterra equation of ecology and the quasispecies equation of molecular evolution.

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Distributed Algorithmic Mechanism Design (DAMD) combines theoretical computer science’s traditional focus on computational tractability with its more recent interest in incentive compatibility and distributed computing. The Internet’s decentralized nature, in which distributed computation and autonomous agents prevail, makes DAMD a very natural approach for many Internet problems. This paper first outlines the basics of DAMD and then reviews previous DAMD results on multicast cost sharing and interdomain routing. The remainder of the paper describes several promising research directions and poses some specific open problems.

Lack of cooperation (free riding) is one of the key problems that confronts today's P2P systems. What makes this problem particularly difficult is the unique set of challenges that P2P systems pose: large populations, high turnover, asymmetry of interest, collusion, zero-cost identities, and traitors. To tackle these challenges we model the P2P system using the Generalized Prisoner's Dilemma (GPD), and propose the Reciprocative decision function as the basis of a family of incentives techniques. These techniques are fully distributed and include: discriminating server selection, maxflowbased subjective reputation, and adaptive stranger policies. Through simulation, we show that these techniques can drive a system of strategic users to nearly optimal levels of cooperation.

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According to conventional wisdom, Nash equilibrium in a game “involves” common knowl-edge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if each player is rational and knows his own payoff function, and the strategy choices of the players are mutually known, then these choices form a Nash equilibrium. The other two results treat the mixed strategies of a player not as conscious randomization of that player, but as conjectures of the other players about what he will do. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures yields Nash equilibrium. When n ≥ 3, mutual knowledge of the payoff functions and of rationality, and common knowl-edge of the conjectures yield Nash equilibrium when there is a common prior. Examples are provided showing these results to be sharp.

Trust is central to all transactions and yet economists rarely discuss the notion. It is treated...

Models of the various adaptive specializations that have evolved in the human psyche could become the building blocks of a scientific theory of culture. The flrst step in creating such models is the derivation of a so-called "computational theory " of the adaptive problem each psychological specialization has evolved to solve. In Part II, as a case study, a sketch of a computational theory of social exchange (cooperation for mutual benefit) is developed. The dynamics of natural selection in Pleistocene ecological conditions define adaptive information processing problems that humans must be able to solve in order to participate in social exchange: individual recognition, memory for one's history of interaction, value communication, value modeling, and a shared gram-mar of social contracts that specifies representational structure and inferential pro-cedures. The nature of these adaptive information processing problems places con-straints on the class of cognitive programs capable of solving them; this allows one to make empirical predictions about how the cognitive processes involved in attention, communication, memory, learning, and reasoning are mobilized in situations of social exchange. Once the cognitive programs specialized for regulating social exchange are mapped, the variation and invariances in social exchange within and between cultures can be meaningfully discussed.

The problem of cooperation1−8 is that defection is evolutionarily stable. If everybody in a population defects and one individual cooperates then this indi-vidual has a lower payoff and will be opposed by selection. Thus, the emergence of cooperation is thought to require specific mechanisms: for example, several cooperators have to arise simultaneously to overcome an invasion barrier9 or arise as spatial clusters10,11. This understanding is based on traditional con-cepts of evolutionary stability and dynamics of infinite populations12−16. Here we study evolutionary game dynamics in finite populations17−20 and show that a single cooperator using a reciprocal strategy3,21 can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions for natural selection to favor the emergence of coopera-tion and derive conditions for evolutionary stability in finite populations. Explaining the evolution of cooperation by natural selection has been a major theme of evolutionary biology since Darwin. The standard game dynamical formulation, which captures the essence of the problem, is the Prisoner’s Dilemma. In the non-repeated game, defection dominates cooperation. In the repeated game, stratetegies like tit-for-tat (TFT) or win-stay, lose-shift allow cooperation, but the question is how do they arise in the first place? Always defect (AllD) is evolutionarily stable against invasion by TFT in traditional game dynamics of infinite populations. Let us investigate a game between two strategies, A and B, with payoff matrix A B A a b