Kybernetika 46 no. 3, 435-446, 2010

Interval valued bimatrix games

Milan Hladík


Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we characterize the set of all possible equilibria by mean of a linear mixed integer system.


bimatrix game, interval matrix, interval analysis


91A05, 91A15, 90C11