Browsing by Subject "Evolutionary game theory"

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  • Berardo, Cecilia; Geritz, Stefanus (2021)
    The war of attrition in game theory is a model of a stand-off situation between two opponents where the winner is determined by its persistence. We model a stand-off between a predator and a prey when the prey is hiding and the predator is waiting for the prey to come out from its refuge, or when the two are locked in a situation of mutual threat of injury or even death. The stand-off is resolved when the predator gives up or when the prey tries to escape. Instead of using the asymmetric war of attrition, we embed the stand-off as an integral part of the predator-prey model of Rosenzweig and MacArthur derived from first principles. We apply this model to study the coevolution of the giving-up rates of the prey and the predator, using the adaptive dynamics approach. We find that the long term evolutionary process leads to three qualitatively different scenarios: the predator gives up immediately, while the prey never gives up; the predator never gives up, while the prey adopts any giving-up rate greater than or equal to a given positive threshold value; the predator goes extinct. We observe that some results are the same as for the asymmetric war of attrition, but others are quite different. (C) 2021 The Author(s). Published by Elsevier Ltd.
  • Hämäläinen, Jani (Helsingin yliopisto, 2018)
    Evolutionary game theory models attempt to explain social norms, which defy rational behaviour, have emerged. This thesis researches if evolutionary game theory model using replicator dynamics can forecast shifts in social norms. Viability of two models from two peer reviewed articles are studied. In “An economist perspective on evolution of norms” by Kenneth Binmore and Larry Samuelson provide learning model using ultimatum game. In “Evolutionary stability and social norms” Rajiv Sethi examines how payoff maximizers fare against norm guided players in prisoner’s dilemma model. Both articles postulate that equilibrium strategies of the models are prevailing social norms of the respective systems. Key concepts of evolutionary game theory are presented. John Maynard Smith and George Price were first to introduce evolutionary stable strategy. If all members of population adept a strategy and no mutant strategy can invade the popula-tion, the original strategy is evolutionarily stable. Stability concept is extended to multi-population systems where repli-cator equations govern dynamics of the systems. Concept of evolutionary stable set is presented. In first of the two models, Binmore and Samuelson describe learning model based on ultimatum game with noise com-ponent. Discrete replicator equations describe dynamics of the model. Binmore and Samuelson find equilibria of the ultimatum game model using several sets of simulations with differing conditions. In the second model Sethi creates two stage prisoner’s dilemma model with eight norms based on pure strategies and payoff maximizers. Continuous replica-tor equations describe dynamics of the model. Sethi finds equilibria of the model analytically. Equilibria of the two models are presented. Study of the equilibria is limited to one simulation in ultimatum game model. In prisoner’s dilemma model study is limited to case where payoff maximizer can identify other strategies. Equilibria of these models is compared to features of social norms. Ultimatum game model removed from further study due lack of multiple equilibria. Long run state of the prisoner’s dilemma model is deterministic. Shifts between social norms do not occur. Stochastic effects are introduced. Stochastic process is added to the prisoner’s dilemma model. Stochastic prisoner’s dilemma model is found to be unsuitable for forecasting. Neither of the presented models can be used for forecasting. Models with best reply dynamics are offered as topic of further research.