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George Price’s Contributions to Evolutionary Genetics
 J. THEOR. BIOL.
, 1995
"... ... Equation, a profound insight into the nature of selection and the basis for the modern theories of kin and group selection; (ii) the theory of games and animal behavior, based on the concept of the evolutionarily stable strategy; and (iii) the modern interpretation of Fisher’s fundamental theore ..."
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Cited by 55 (8 self)
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... Equation, a profound insight into the nature of selection and the basis for the modern theories of kin and group selection; (ii) the theory of games and animal behavior, based on the concept of the evolutionarily stable strategy; and (iii) the modern interpretation of Fisher’s fundamental theorem of natural selection, Fisher’s theorem being perhaps the most cited and least understood idea in the history of evolutionary genetics. This paper summarizes Price’s contributions and briefly outlines why, toward the end of his painful intellectual journey, he chose to focus his deep humanistic feelings and sharp,
Evolutionary Game Dynamics in Finite Populations
, 2004
"... We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are ..."
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Cited by 46 (12 self)
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We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.
The Algebra of Assortative Encounters and the Evolution of Cooperation
 International Game Theory Review
"... This paper has benefited from comments by participants in the Evolutionary Game Theory workshop held at the University of Odense, Denmark in September 2000 and a workshop on Groups, Multilevel Selection and Economic Dynamics, held at the Santa Fe Institute in January of 2001. Special thanks for hel ..."
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Cited by 21 (7 self)
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This paper has benefited from comments by participants in the Evolutionary Game Theory workshop held at the University of Odense, Denmark in September 2000 and a workshop on Groups, Multilevel Selection and Economic Dynamics, held at the Santa Fe Institute in January of 2001. Special thanks for helpful remarks are due to Marc Feldman, Hillard Kaplan,Thorbjørn Knudsen, Chris Proulx, and Consider a population of individuals who meet and play Prisoners ’ Dilemma. Players do not deliberately choose their strategies, but are “programmed ” to play either cooperate or defect. In Prisoners ’ Dilemma, everyone gets a higher payoff from playing defect than from playing cooperate, but everyone gets
Stochastic Evolution as a Generalized Moran Process” Working Paper
, 2004
"... This paper proposes and analyzes a model of stochastic evolution in finite populations. The expected motion in our model resembles the standard replicator dynamic when the population is large, but is qualitatively different when the population size is small, due to the difference between maximizing ..."
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Cited by 3 (2 self)
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This paper proposes and analyzes a model of stochastic evolution in finite populations. The expected motion in our model resembles the standard replicator dynamic when the population is large, but is qualitatively different when the population size is small, due to the difference between maximizing payoff and maximizing relative payoff. Moreover, even in large populations the asymptotic behavior of our system differs from that of the bestresponse and replicator dynamics due to its stochastic component.
Comparative Statics of Games Between Relatives
, 2005
"... According to Hamilton’s theory of kin selection, species tend to evolve behavior such that each organism appears to be attempting to maximize its inclusive fitness. In particular, two neighbors are likely to help each other if the cost of doing so is less than the benefit multiplied by r, their coef ..."
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Cited by 1 (0 self)
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According to Hamilton’s theory of kin selection, species tend to evolve behavior such that each organism appears to be attempting to maximize its inclusive fitness. In particular, two neighbors are likely to help each other if the cost of doing so is less than the benefit multiplied by r, their coefficient of relatedness. Since the latter is less than unity, mutual altruism benefits both neighbors. However, is it theoretically possible that acting so as to maximize the inclusive, rather than personal, fitness may harm both parties. This may occur in strategic symmetric pairwise interactions (more specifically, n × n games), in which the outcome depends on both sides ’ actions. In this case, the equilibrium outcome may be less favorable to the interactants ’ personal fitness than if each of them acted so as to maximize the latter. This paper shows, however, that such negative effect of relatedness on fitness is incompatible with evolutionary stability. If the symmetric equilibrium strategies are evolutionarily stable, a higher coefficient of relatedness can only entail higher personal fitness for the two neighbors. This suggests that negative comparative statics as above are not likely to occur in nature.
Convergence in the Finite Cournot Oligopoly with Social and Individual Learning
, 2009
"... Convergence to the Nash equilibrium in a Cournot oligopoly is a question that recurrently arises as a subject of controversy in economics. The development of evolutionary game theory has provided an equilibrium concept more directly connected with adjustment dynamics, and the evolutionary stability ..."
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Cited by 1 (1 self)
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Convergence to the Nash equilibrium in a Cournot oligopoly is a question that recurrently arises as a subject of controversy in economics. The development of evolutionary game theory has provided an equilibrium concept more directly connected with adjustment dynamics, and the evolutionary stability of the equilibria of the Cournot game has been extensively studied in the literature. Several articles show that the Walrasian equilibrium is the stable ESS of the Cournot game. But no general result has been established for the difficult case of simultaneous heterogenous mutations. Authors propose specific selection dynamics to analyze this case. Vriend (2000) proposes using a genetic algorithm for studying learning dynamics in this game and obtains convergence to Cournot equilibrium with individual learning. The resulting convergence has been questioned by Arifovic and Maschek (2006). The aim of this article is to clarify this controversy: it analyzes the mechanisms that are behind these contradictory results and underlines the specific role of the spite effect. We show why social learning gives rise to the Walrasian equilibrium and why, in a general setup, individual learning can effectively yield convergence to the Cournot equilibrium. We also illustrate these general
The Spite Motive and Equilibrium Behavior in
"... reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress, which has been given certain exclusive rights by the author. Contributions to Economic ..."
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reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress, which has been given certain exclusive rights by the author. Contributions to Economic Analysis & Policy is produced by The Berkeley Electronic Press (bepress).
and the Evolution of Cooperation
, 2001
"... This paper explores the quantitative relation between non random, assortative matching and the maintenance of cooperative behavior under evolutionary dynamics. We consider a population of individuals who are \hardwired” to play either cooperate or defect. They meet other individuals according to som ..."
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This paper explores the quantitative relation between non random, assortative matching and the maintenance of cooperative behavior under evolutionary dynamics. We consider a population of individuals who are \hardwired” to play either cooperate or defect. They meet other individuals according to some random process and play their programmed strategy in a game of Prisoners’ Dilemma. The type that gets the higher expected payoff reproduces more rapidly. We dēne an index of assortativity of encounters and develop an \algebra of assortative encounters. ” In one set of applications, we calculate the index of assortativity for games between relatives with either cultural or genetic inheritance and we show the logical connection between the index of assortativity and Hamilton’s theory of kin selection [5]. We also apply the index of assortativity to determine the population dynamics when players select their partners, using