On characterizing equilibrium points in two person strictly competitive games (Q790057)

A two-person game is strictly competitive if for all strategies s and s', \(P_ 1(s)\geq P_ 1(s')\) if and only if \(P_ 2(s)\leq P_ 2(s')\), where \(P_ i\) is the payoff function to player i, \(i=1,2\). The paper shows that for such games the set of equilibrium strategies for each player is convex (and as has been shown before, equilibrium pairs are interchangeable).