As a special case of symmetric game in which the players share a common payoff matrix, evolutionary game provides a suitable approach to model and explore the emergence of cooperative behavior in natural and social systems. The evolutionary spatial game (ESG) further specifies the payoff for each individual by both the payoff matrix M and the spatial dependence structure of the population on a geophysical domain. Two players game serves as a foundation of modeling various biological/social interactive systems and provides a great amount of interesting game theoretical models such as prisoner's dilemma game, snow drift game etc.
We formulate a two players evolutionary spatial game under the framework of initialization, effective local payoff, and the Markov chain for strategy update. The spatial dependence structure is modeled by a probability distribution parameterized by the dependence geometry and strength in the neighborhood of each location. Particularly, we study the structure based on Gaussian process. Computational methods are proposed and applied to study the convergence of simulations. In addition, limiting non-local differential equation is introduced and analysed in terms of spreading speeds and traveling waves.</p
