Equilibrium Identification and Selection in Finite Games

Abstract

Decision-making under simultaneous competition Hardly any decision is made in isolation and most decision makers are dealing with fierce competition when trying to find the optimal decision for their problem. The expected outcome of such a competitive problem setting or the individually optimal course of action for each competitor is not evident. In a finite game, a finite set of decision makers simultaneously select their action from a finite set of strategies. In “Equilibrium identification and selection in finite games”, T. Crönert and S. Minner propose a solution approach enumerating all equilibria and selecting the most likely equilibrium in finite games. The approach is targeted toward large finite games that cannot be efficiently represented in normal form. They apply their algorithm to two- and three-player knapsack and facility location and design games. Their numerical experiments show that prior approaches identifying a single equilibrium can result in unlikely outcomes.