The paper presents an attempt to integrate the classical evolutionary game theory based on replicator dynamics and state-based approach of Houston McNamara. In new approach, individuals have different heritable strategies; however, carrying same strategy can differ in terms state, role or situation which they act. Thus, is completed by additional subsystem differential equations describing tran...

This paper rigorously justifies the approximation of aggregate imitational behavior in large populations by the deterministic dynamics given by Bjönerstedt and Weibull. We first clarify what models fit their formulation, in which the stochastic dynamics depends only on the average frequencies of strategies in populations. Then we show that the stochastic process of each individual’s behavior co...

The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator equation are given including a discussion of information divergences, evolutionary stability, and exponential families as solutions for the replicator dynamic, usin...

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for tran-sience is given in terms of mixed equilibria and definiteness of t...

Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable, either caused by external environment or intrinsic random competitions in finite populations, and the evolutionary dynamics is stochastic in nature. Here we show ...

Norm formation is one of the most basic processes of social interaction. To clarify this process, we introduce mutual commitment and meta commitment among agents. R. Axelrod has analyzed the commitment structure of norm formation and the collapsing process of the norm as his norm and meta norm games [1] . He analyzes the games with genetic algorithm. In this paper we generalize the games as mut...

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open. Here we exa...

We propose a first-order interior-point method for linearly constrained smooth optimization that unifies and extends first-order affine-scaling method and replicator dynamics method for standard quadratic programming. Global convergence and, in the case of quadratic program, (sub)linear convergence rate and iterate convergence results are derived. Numerical experience on simplex constrained pro...