Two and three person games: A local study

Abstract

Using the tools of differential geometry two-person games in normal form and their “ordinary” points, i.e. the points which are not equilibria in any sense, are studied. The concept of reversibility if defined and characterized in terms of the derivatives of the payoff functions. Reversible points appear as those points at which the behavior may become cooperative. In the second part of the paper, three-person games in normal form are considered. All the concepts defined depend only on the preference preorderings associated with the payoff functions and do not depend on the metric of the strategy spaces.