Large Population Limits for Evolutionary Dynamics with Random Matching

Molzon, Robert

doi:10.1007/s13235-011-0037-0

Dyn Games Appl

2011

DOI: 10.1007/s13235-011-0037-0

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Large Population Limits for Evolutionary Dynamics with Random Matching

Robert Molzon

Abstract: A frequent assumption in evolutionary game theory is that the population size is sufficiently large so that matching of players is essentially deterministic and payoffs are determined by the expected value of a random match. This paper studies the assumption in the context of a well known model of Kandori, Malaith, and Rob. As the population size tends to infinity, the stationary distribution of an evolutionary process defined by a class of two strategy-two player games with random matching of players fails to… Show more

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2018

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Cited by 2 publications

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Effects of sampling interaction partners and competitors in evolutionary games

Hauert

Miękisz

2018

Phys. Rev. E

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The sampling of interaction partners depends on often implicit modelling assumptions, yet has marked effects on the dynamics in evolutionary games. One particularly important aspect is whether or not competitors also interact. Population structures naturally affect sampling such that in a microscopic interpretation of the replicator dynamics in well-mixed populations competing individuals do not interact but do interact in structured populations. In social dilemmas interactions with competitors invariably inhibit cooperation while limited local interactions in structured populations support cooperation by reducing exploitation through cluster formation. These antagonistic effects of population structures on cooperation affect interpretations and the conclusions depend on the details of the comparison. For example, in the Snowdrift game, spatial structure may inhibit cooperation when compared to the replicator dynamics. However, modifying the replicator dynamics to include interactions between competitors lowers the equilibrium frequency of cooperators, which changes the conclusions and space is invariably beneficial, just as in the Prisoner's Dilemma. These conclusions are confirmed by comparisons with random matching models, which mimic population structures but randomly reshuffle individuals to inhibit spatial correlations. Finally, the differences in the dynamics with and without interactions among competing individuals underlies the differences between death-birth and birth-death updating in the spatial Moran process: death-birth supports cooperation because competitors tend not to interact whereas they tend to do for birth-death updating and hence cooperators provide direct support to competitors to their own detriment.

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Effects of sampling interaction partners and competitors in evolutionary games

Hauert

Miękisz

2018

Phys. Rev. E

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Orders of limits for stationary distributions, stochastic dominance, and stochastic stability

Sandholm

2010

Theoretical Economics

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A population of agents recurrently plays a two-strategy population game. When an agent receives a revision opportunity, he chooses a new strategy using a noisy best response rule that satisfies mild regularity conditions; best response with mutations, logit choice, and probit choice are all permitted. We study the long run behavior of the resulting Markov process when the noise level η is small and the population size N is large. We obtain a precise characterization of the asymptotics of the stationary distributions μ N η as η approaches zero and N approaches infinity, and we establish that these asymptotics are the same for either order of limits and for all simultaneous limits.In general, different noisy best response rules can generate different stochastically stable states. To obtain a robust selection result, we introduce a refinement of risk dominance called stochastic dominance, and we prove that coordination on a given strategy is stochastically stable under every noisy best response rule if and only if that strategy is stochastically dominant.

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Large Population Limits for Evolutionary Dynamics with Random Matching

Cited by 2 publications

References 15 publications

Effects of sampling interaction partners and competitors in evolutionary games

Effects of sampling interaction partners and competitors in evolutionary games

Orders of limits for stationary distributions, stochastic dominance, and stochastic stability

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