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39
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 105 (1 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 48 (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.
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 20 (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
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 sensible learning ru ..."
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Cited by 9 (5 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.
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 6 (0 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.
Honey Bee Social Foraging Algorithms for Resource Allocation: Theory And Application
, 2010
"... ..."
Evolutionary dynamics of finite populations in games with polymorphic fitnessequilibria
 Journal of Theoretical Biology. forthcoming
, 2007
"... The HawkDove (HD) game, as defined by Maynard Smith (1982), allows for a polymorphic fitnessequilibrium (PFE) to exist between its two pure strategies; this polymorphism is the attractor of the standard replicator dynamics (Taylor and Jonker, 1978; Hofbauer and Sigmund, 1998) operating on an infin ..."
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Cited by 5 (3 self)
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The HawkDove (HD) game, as defined by Maynard Smith (1982), allows for a polymorphic fitnessequilibrium (PFE) to exist between its two pure strategies; this polymorphism is the attractor of the standard replicator dynamics (Taylor and Jonker, 1978; Hofbauer and Sigmund, 1998) operating on an infinite population of purestrategists. Here, we consider stochastic replicator dynamics, operating on a finite population of purestrategists playing games similar to HD; in particular, we examine the transient behavior of the system, before it enters an absorbing state due to sampling error. Though stochastic replication prevents the population from fixing onto the PFE, selection always favors the underrepresented strategy. Thus, we may naively expect that the mean population state (of the preabsorption transient) will correspond to the PFE. The empirical results of Fogel et al. (1997) show that the mean population state, in fact, deviates from the PFE with statistical significance. We provide theoretical results that explain their observations. We show that such deviation away from the PFE occurs when the selection pressures that surround the fitnessequilibrium point are asymmetric. Further, we analyze a Markov model to prove that a finite population will generate a distribution over population states that equilibrates selectionpressure asymmetry; the mean of this distribution is generally not the fitnessequilibrium state.
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 4 (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,
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.