Absolute optimal solution for a compact and convex game

This paper investigates the existence of absolute optimal solutions for a partition P in continuous and quasiconcave games. We show that the P -consistence property introduced in the paper, together with the quasiconcavity and continuity of payoffs, permits the existence of P -absolute optimal solutions in games with compact and convex strategy spaces. The P consistency property is a general condition that cannot be dispensed with for the existence of P -absolute optimal solutions. We also characterize the existence of P -absolute optimal solutions by providing necessary and sufficient conditions. Moreover, we suggest an algorithm for efficiently computing P -absolute optimal solutions.