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Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computationally intractable. The approach is to generate the normal form of the game (the matrix containing the payoff for each strategy combination), and then solve a linear program (LP) or a linear complementarity problem (LCP). The size of the normal form, however, is typically exponential in the size of the game tree, thus making this method impractical in all but the simplest cases. This paper describes a new representation of strategies which results in a practical linear formulation of the problem of two-player games with perfect recall (i.e., games where players never forget anything, which is a standard assumption). Standard LP or LCP solvers can then be applied to find optimal randomized strategies. The resulting algorithms are, in general, exponentially better than the standard ones, both in terms of time and in terms of space.

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition arising naturally in models of network congestion. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to equilibrium from all initial conditions. We propose a subclass of potential games in which evolution leads to efficient play. Finally, we show that the games studied here are the limits of convergent sequences of the finite player potential games studied by Monderer and Shapley (1996).

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that allows to choose the direction for the next step at random from all directions along which fitness does not decrease. Stationary states of populations correspond to local optima of the fitness landscape. Evolution is seen as a series of transitions between optima with increasing fitness values. Wright's metaphor saw a recent revival when sufficiently simple models of fitness landscapes became available [1, 41]. These models are based on spin glass theory [63, 66] or closely related to it like Kauffman's Nk model [42]. Evolution of RNA molecules has been studied by more realistic models that deal explicitly with molecular structures obtained from folding RNA sequences [23, 24]. Fitness values serving as input parameters for evolutionary dynamics were derived through evaluation of the structures. The complexity of RNA fitness landscapes originates from conflicting consequences of structural changes that are reminiscent of "frustration" in the theory of spin glasses [2]. Fitness in t

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations—a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.

This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equilibria that specify the same behavior on the equilibrium path, but different out-of-equilibrium behavior, appear in connected components of stationary states. The stability properties of these components often depend critically on the perturbations to which the system is subjected. We argue that it is then important to incorporate such drift into the model. A su±cient condition is provided for drift to create stationary states with strong stability properties near a component of equilibria. This result is used to derive comparative static predictions concerning common questions raised in the literature on refinements of Nash equilibrium

This paper describes an evolutionary method for identifying the gene regulatory network from the observed time series data of the gene's expression. We use a system of ordinary differential equations as a model of the network and infer their right-hand sides by using Genetic Programming (GP). To explore the search space more effectively in the course of evolution, the least mean square (LMS) method is used along with the ordinary GP. We apply our method to three target networks and empirically show how successfully GP infers the systems of differential equations.

The success of Artificial Life depends on whether it will help solving the conceptual problems of biology. Biology may be viewed as the science of the transformation of organizations. And, yet, biology lacks a theory of organization. We use this as an example of the challenge that Artificial Life must meet. "If - as I believe - physics and chemistry are conceptually inadequate as a theoretical framework for biology, it is because they lack the concept of function, and hence that of organization. [...] [P]erhaps, therefore, we should give the [...] computer scientists more of a say in the formulation of Theoretical Biology." -- Christopher Longuet-Higgins, 1969 [29] 1 Life and the organization problem in biology There are two readings of "life": "life" as an embodied phenomenon and "life" as a concept. Foucault [20] points out that up to the end of the eighteenth century life does not exist: only living beings. Living beings are but a class in the series of all things in the world. T...

A model of population rule learning is formulated and estimated using experimental data. When predicting the population distribution of choices and accounting for the number of parameters, the population rule learning model is much better than aggregation of individually estimated rule learning models. Further, rule learning is a statistically significant and important phenomena even when focusing on population statistics, and is much better than one-rule learning dynamics. 2001 Elsevier Science B.V. All rights reserved. JEL classification: C15; C52; C72 Keywords: Rules; Learning; Games; Experimental; Testing 1. Introduction Recent learning research in one-shot games can be divided into two domains: (i) population learning or evolutionary dynamics as typified by replicator dynamics, 1 and (ii) individual learning. 23 The first domain focuses on how the population distribution of play changes over time, while the second domain focuses on how an individual's behavior changes over...