Abstract. Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In this survey, we present an overview of the many brands of deterministic dynamical systems motivated by evolutionary game theory, including ordinary differential equations (and, in particular, the replicator equation), differential inclusions (the best response dynamics), difference equations (as, for instance, fictitious play) and reaction-diffusion systems. A recurrent theme (the so-called ‘folk theorem of evolutionary game theory’) is the close connection of the dynamical approach with the Nash equilibrium, but we show that a static, equilibriumbased viewpoint is, on principle, unable to always account for the long-term behaviour of players adjusting their behaviour to maximise their payoff. 1.

Most contracts, whether between voters and politicians or between house owners and contractors, are incomplete. “More law,” it typically is assumed, increases the likelihood of contract performance by increasing the probability of enforcement and/or the cost of breach. This paper studies a contractual relationship where the first mover has to decide whether she wants to enter a contract without knowing whether the second mover will perform. We analyze how contract enforceability affects individual performance for exogenous preferences. Then we apply a dynamic model of preference adaptation and find that economic incentives have a non–monotonic impact on behavior. Individuals perform a contract when enforcement is strong or weak but not with medium enforcement probabilities: Trustworthiness is “crowded in” with weak and “crowded out” with medium enforcement. In a laboratory experiment we test our model’s implications and find support for the crowding prediction. Our finding is in line with the recent work on the role of contract enforcement and trust in formerly Communist countries.

This paper therefore builds on [3], in which a model of consistent aspirations-based learning was introduced

This paper studies decision-making with rules of thumb in the context of dynamic decision problems and compares it to dynamic programming. A rule is a fixed mapping from a subset of states into actions. Rules are compared by averaging over past experiences. This can lead to favoring rules which are only applicable in good states. Correcting this good state bias requires solving the dynamic program. We provide a general framework and characterize the asymptotic properties. We apply it to provide a candidate explanation for the sensitivity of consumption to transitory income.

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This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes.

We address the problem of learning and implementation in the Internet. When agents play repeated games in distributed environments like the Internet, they have very limited a priori information about the other players and the payo matrix. Consequently, standard solution concepts like Nash equilibria, or even the serially undominated set, do not apply in such a setting. To construct more appropriate solution concepts, we rst describe the essential properties that constitute \reasonable " learning behavior in distributed environments. We then study the convergence behavior of such algorithms; these results lead us to propose rather non traditional solutions concepts for this context. Finally, we discuss implementation of social choice functions with these solution concepts, and nd that only strictly coalitionally strategyproof social choice functions are implementable. 1 1

The mechanism design problem in economics is about designing rules of interaction for market games so they yield a globally desirable result in the face of self-interested agents. This problem, which is of importance for ecommerce since much ecommerce is carried out through auctions, can be extremely complex. Traditionally, economists have tried using game theory and other formal methods to construct suitable mechanism rules. However, analytical methods typically oversimplify the problem and so the resulting rules are not necessarily robust. In this paper, we report on an alternative approach which we hope will eventually yield more robust solutions. Our methodology views mechanism design as a multi-objective optimisation problem and addresses the problem using genetic programming.

. The experimental phenomenon known as "probability matching" is often offered as evidence in support of adaptive learning models and against the idea that people maximise their expected utility. Recent interest in dynamic-based equilibrium theories means the term re-appears in Economics. However, there seems to be conflicting views on what is actually meant by the term and about the validity of the data. The purpose of this paper is therefore threefold: First, to introduce today's readers to what is meant by probability matching, and in particular to clarify which aspects of this phenomenon challenge the utility-maximisation hypothesis. Second, to familiarise the reader with the different theoretical approaches to behaviour in such circumstances, and to focus on the differences in predictions between these theories in light of recent advances. Third, to provide a comprehensive survey of repeated, binary choice experiments. Keywords. Probability Matching; Stochastic Learning; Optimis...

This paper describes the results of simulation experiments performed on a suite of learning algorithms. We focus on games in network contexts. These are contexts in which (1) agents have very limited information about the game; (2) play can be extremely asynchronous. There are many proposed learning algorithms in the literature. We choose a small sampling of such algorithms and use numerical simulation to explore the nature of asymptotic play. In particular, we explore the extent to which the asymptotic play depends on three factors, namely: limited information, asynchronous play, and the degree of responsiveness of the learning algorithm.