A noncooperative game on polyhedral sets

A problem of a Nash equilibrium point existence and calculating in a noncooperative two-person game on generally unbounded polyhedral sets with the payoff functions of two vector arguments being those of maximum of finite numbers of linear functions is considered. It is shown that the problem is reducible to that in an auxiliary two-person zero-sum game on a polyhedral set of connected strategies with the payoff function being a sum of two linear ones. For the latter game verifiable, necessary, and sufficient conditions of its Nash equilibrium points that allow calculating the points by solving a system of linear and quadratic constraints were proposed by the author in [1].