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55
On the Global Convergence of Stochastic Fictitious Play
 ECONOMETRICA
, 2002
"... We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stocha ..."
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Cited by 52 (10 self)
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We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.
Exploring bidding strategies for marketbased scheduling
 DECISION SUPPORT SYSTEMS
, 2005
"... ..."
Landscapes And Molecular Evolution
, 1996
"... 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. ..."
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Cited by 42 (6 self)
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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
Artificial Chemistries  A Review
, 2000
"... This article reviews the growing body of scientific work in Artificial Chemistry. First, common motivations and fundamental concepts are introduced. Second, current research activities are discussed along three application dimensions: modelling, information processing and optimization. Finally, comm ..."
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Cited by 34 (4 self)
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This article reviews the growing body of scientific work in Artificial Chemistry. First, common motivations and fundamental concepts are introduced. Second, current research activities are discussed along three application dimensions: modelling, information processing and optimization. Finally, common phenomena among the different systems are summarized. It is argued here that Artificial Chemistries are "the right stuff" for the study of prebiotic and biochemical evolution, and they provide a productive framework for questions regarding the origin and evolution of organizations in general. Furthermore, Artificial Chemistries have a broad application range to practical problems as shown in this review.
Beyond Digital Naturalism
, 1994
"... 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 mu ..."
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Cited by 29 (1 self)
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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 LonguetHiggins, 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...
Random Catalytic Reaction Networks
, 1993
"... We study networks that are a generalization of replicator (or LotkaVolterra) equations. They model the dynamics of a population of object types whose binary interactions determine the specific type of interaction product. We show that the system always reduces its dimension to a subset that contain ..."
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Cited by 25 (3 self)
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We study networks that are a generalization of replicator (or LotkaVolterra) equations. They model the dynamics of a population of object types whose binary interactions determine the specific type of interaction product. We show that the system always reduces its dimension to a subset that contains production pathways for all of its members. The network equation can be rewritten at a level of collectives in terms of two basic interaction patterns: replicator sets and cyclic transformation pathways among sets. Although the system contains wellknown cases that exhibit very complicated dynamics, the generic behavior of randomly generated systems is found (numerically) to be extremely robust: convergence to a globally stable rest point. It is easy to tailor networks that display replicator interactions where the replicators are entire selfsustaining subsystems, rather than structureless units. A numerical scan of random systems highlights the special properties of elementary replicator...
Notes on equilibria in symmetric games
 In Proceedings of the 6th International Workshop On Game Theoretic And Decision Theoretic Agents (GTDT
, 2004
"... In a symmetric game, every player is identical with respect to the game rules. We show that a symmetric 2strategy game must have a purestrategy Nash equilibrium. We also discuss Nash’s original paper and its generalized notion of symmetry in games. As a special case of Nash’s theorem, any finite sy ..."
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Cited by 24 (6 self)
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In a symmetric game, every player is identical with respect to the game rules. We show that a symmetric 2strategy game must have a purestrategy Nash equilibrium. We also discuss Nash’s original paper and its generalized notion of symmetry in games. As a special case of Nash’s theorem, any finite symmetric game has a symmetric Nash equilibrium. Furthermore, symmetric infinite games with compact, convex strategy spaces and continuous, quasiconcave utility functions have symmetric purestrategy Nash equilibria. Finally, we discuss how to exploit symmetry for more efficient methods of finding Nash equilibria. 1.