On games with stochastically dependent strategies

Bimatrix games under the supposition of dependent randomization devices realizing the mixed strategies of players are considered (e.g. the players may use the same pseudorandom numbers generator). The paper analyzes the structure of possible types of dependence, examines the structure of Nash Equilibria sets yielded by these types and shows that the unique type of dependence for which any matrix game has a Nash Equilibrium is stochastic independence.