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Abstract Evolutionary game dynamics has become a hot topic in recent years. In this paper, we combine game theory and dynamical systems to investigate the stability of imitative dynamics in two-community with different kinds of delays. First, we establish a new model of imitative dynamics in two-community. Then, three sufficient conditions of the asymptotical stability for the neutrally stable strategy of the imitative dynamics are obtained. Finally, numerical simulations are consistent with the theoretical analysis.

Evolutionary game dynamics is a combination of game theory and dynamical systems. Using dynamical theory, we investigate chaotic behavior in asymmetric Rock-Paper-Scissors games under imitative dynamics with two different populations. Our theoretical analysis and numerical simulations demonstrate that the dynamical system can give rise to chaotic behavior in zero-sum and positive-sum asymmetric games. However, chaos cannot occur in a negative-sum asymmetric game. In particular, the numerical simulations show that there is a limit cycle in a negative-sum asymmetric game.

Evolutionary game dynamics has become a hot topic in recent years. In this paper, we combine game theory and dynamical systems to investigate the stability of imitative dynamics in two-community with different kinds of delays. First, we establish a new model of imitative dynamics in two-community. Then, three sufficient conditions of the asymptotical stability for the neutrally stable strategy of the imitative dynamics are obtained. Finally, numerical simulations are consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studies imitative dynamics for games with continuous strategy space. We define imitative dynamics—which include the replicator dynamic as a special case—as evolutionary dynamics that satisfy the imitative property and payoff monotonicity. Our definition of payoff monotonicity, which we use Radon–Nikodym derivatives to define, is weaker than the one proposed in Oechssler and Riedel (2002) . We find that Oechssler and Riedel (2002) 's definition is too strong, and our definition is more adequate than theirs. We show that for a broad class of payoff functional dynamics, payoff monotonicity à la Oechssler and Riedel (2002) is equivalent to aggregate monotonicity in the sense of Samuelson and Zhang (1992) . We then provide sufficient conditions for imitative dynamics and general evolutionary dynamics to be well-defined. Finally, with our definition of payoff monotonicity, a number of results that are standard for finite games extend to the case of games with continuous strategy space. [ABSTRACT FROM AUTHOR]