Evolution and equilibrium under inexact information. (Q1408715)

The article is devoted to a general model of stochastic evolution in games. Let \(X_t^N=\{(R_t^N,U_t^N)\}_{t\geq 0}\) be the behavior process describing the proportions of players in a population of \(N\) individuals choosing strategies \(R\) and \(U\). The author defines the local behavior process at \(x^*\) \(Z_t^N=\sqrt{N}(X_t^N-x^*)\) and admits that it satisfies the stochastic differential equation \(dZ_t=DZ_tdt+\frac{1}{\sqrt{2}}IdB_t\) where \(D\) is a linear operator and \(B_t\) denotes white noise. A new notion of stability called local probabilistic stability (LPS) is proposed, which requires that a population which begins to play in equilibrium settles into a fixed stochastic pattern around the equilibrium. Then LPS is compared with standard deterministic notions of stability.