Characterization of optimal strategies in matrix games with convexity properties (Q1423659)

Let \(G\) be an \(n\)-player matrix game in normal form. The paper gives a new proof for the existence of pure strategy equilibrium of \(G\), using the notions of row-quasiconvexity and column-quasi-concavity. The paper also gives a characterization of mixed strategy equilibrium of \(G\). The latter result is a follow up to \textit{L. Shapley} [Ann. Math. Stud. 52, 1--28 (1964; Zbl 0126.16204) and ibid. 52, 267--305 (1964; Zbl 0126.16303)].