Browsing by Subject "Stochastic effects"

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.