Leads to a natural definition of stochastic dynamics in Game Theory. His utility function ui depends on his own strategy as well as on others'. Each player continuously adjusts his variable in order to maximize his utility. He also faces stochastic shocks and so his variable becomes a continuous time stochastic process. We focus on a particular class of games with global interaction.
Nash equilibria are stationary points of the dynamics.
Game Theory and Evolution Large number of interacting agents. Each agent has a spectrum of strategies and a utility or payoff function, which depends on the strategy. Game Theory assumes that payoff functions are common knowledge and that each player behaves rationally. Stable states of the system are called Nash Equilibria. The NE strategies are then such that no player has incentives to change them, since any change would result in utility loss.