Minimality of consistent solutions for strategic games, in particular for potential games

Solutions defined on classes of strategic games, satisfying One-Person Rationality (OPR), Non-emptiness (NEM) and Consistency (CONS) are considered. The main question to be answered is whether these conditions characterize the Nash Equilibrium solution NE for the given class of games. Depending on the structure of the class of games positive as well as negative answers are obtained. A graph-theoretical framework will be developed to express sufficient conditions for a positive or a negative answer. For the cass of (finite) strategic games with at least one Nash equilibrium the answer is positive. For several classes of potential games the answer is negative.