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79
Emergence of cooperation and evolutionary stability in finite populations. Nature
, 2004
"... The problem of cooperation1−8 is that defection is evolutionarily stable. If everybody in a population defects and one individual cooperates then this individual has a lower payoff and will be opposed by selection. Thus, the emergence of cooperation is thought to require specific mechanisms: for ex ..."
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Cited by 175 (27 self)
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The problem of cooperation1−8 is that defection is evolutionarily stable. If everybody in a population defects and one individual cooperates then this individual 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 concepts 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 cooperation 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 nonrepeated game, defection dominates cooperation. In the repeated game, stratetegies like titfortat (TFT) or winstay, loseshift 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
Speculation Duopoly with Agreement to Disagree: Can Overconfidence Survive the Market Test?
 Journal of Finance
, 1997
"... In a duopoly model of informed speculation, we show that overconfidence may strictly dominate rationality since an overconfident trader may not only generate higher expected profit and utility than his rational opponent, but also higher than if he were also rational. This occurs because overconfiden ..."
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Cited by 173 (2 self)
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In a duopoly model of informed speculation, we show that overconfidence may strictly dominate rationality since an overconfident trader may not only generate higher expected profit and utility than his rational opponent, but also higher than if he were also rational. This occurs because overconfidence acts like a commitment device in a standard Cournot duopoly. As a result, for some parameter values the Nash equilibrium of a twofund game is a Prisoner's Dilemma in which both funds hire overconfident managers. Thus, overconfidence can persist and survive in the long run. 2 The rational expectations hypothesis implies that economic agents make decisions as though they know a correct probability distribution of the underlying uncertainty. According to the traditional view (Alchian (1950) and Friedman (1953)), the rational expectations hypothesis is empirically plausible because rational beliefs are better able to survive the market test than irrational beliefs. Yet, the empirical liter...
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 95 (15 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.
An ‘‘evolutionary’’ interpretation of Van Huyck, Battalio, and Beil’s experimental results on coordination
 Games Econ. Behav
, 1991
"... This paper proposes an adaptive interpretation of the results of some recent experiments with repeated tacit coordination games. These experiments revealed several behavioral regularities, including a systematic discrimination between strict Nash equilibria in certain games, that appear to be driven ..."
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Cited by 35 (0 self)
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This paper proposes an adaptive interpretation of the results of some recent experiments with repeated tacit coordination games. These experiments revealed several behavioral regularities, including a systematic discrimination between strict Nash equilibria in certain games, that appear to be driven by strategic uncertainty, and are not explained by traditional equilibrium refinements. The observed patterns of discrimination correspond closely to predictions based on Maynard Smith’s notion of evolutionary stability. An adaptive model, in the spirit of the evolutionary dynamics but recognizing the important differences between learning in human populations and evolution, promises to yield a unified explanation
Evolutionary stability on graphs
, 2008
"... Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect e ..."
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Cited by 13 (1 self)
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Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k42. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth–death (BD), death–birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a wellmixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs.
Stochastic Evolution as a Generalized Moran Process
, 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 13 (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.
Cournot versus Walras in dynamic oligopolies with memory
, 2001
"... This paper explores the impact of memory in Cournot oligopolies where firms learn through imitation of success (as suggested in Alchian (1950) and modeled in VegaRedondo (1997)). As long as memory includes at least one period, the longrun outcomes correspond to all the quantities in the interval b ..."
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Cited by 11 (0 self)
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This paper explores the impact of memory in Cournot oligopolies where firms learn through imitation of success (as suggested in Alchian (1950) and modeled in VegaRedondo (1997)). As long as memory includes at least one period, the longrun outcomes correspond to all the quantities in the interval between the Cournot quantity and the Walras one. There is a conceptual tension between the evolutionary stability associated to the walrasian outcome, which relies on interfirm comparisons of simultaneous profits, and the stability of the CournotNash equilibrium,
Learning and MixedStrategy Equilibria in Evolutionary Games
 Model,” J. Theoret. Bid
, 1989
"... This paper considers whether Maynard Smith's concept of an evolutionarily stable strategy, or "ESS", can be used to predict longrun strategy frequencies in large populations whose members are randomly paired to play a game, and who adjust their strategies over time according to sensi ..."
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Cited by 10 (3 self)
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This paper considers whether Maynard Smith's concept of an evolutionarily stable strategy, or "ESS", can be used to predict longrun strategy frequencies in large populations whose members are randomly paired to play a game, and who adjust their strategies over time according to sensible learning rules. The existing results linking the ESS to stable equilibrium population strategy frequencies when strategies are inherited do not apply to learning, even when each individual always adjusts its strategy in the direction of increased fitness, because the inheritedstrategies stability results depend on aggregating across individuals, and this is not possible for learning. The stability of learning must therefore be analyzed for the entire system of individuals ' strategy adjustments. The interactions between individuals' adjustments prove to be generically destabilizing at mixedstrategy equilibria, which are saddlepoints of the learning dynamics. Using the inheritedstrategies dynamics to describe learning implicitly restricts the system to the stable manifold whose trajectories approach the saddlepoint, masking its instability. Thus, allowing for the interactions between individuals ' strategy adjustments extends the widely recognized instability of mixedstrategy equilibria in multispecies inheritedstrategies models to singlespecies (or multispecies) learning models. I.