Remarks on acyclic versions of generalized von Neumann and Nash equilibrium theorems

A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized “onNeumann type intersection theorems, the Nash type equilibrium theorems, and the “onNeumann minimax theorem. Our new results generalize earlier works of Lassonde [l], Simons [2], and Park [3,4]. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Kakutani map, Acyclic map, Admissible subset (in the sense of Klee), Coincidence, Intersection theorem, Equilibrium theorem, Saddle point, Minimax theorem.