On the structure of the set of Nash equilibria of weakly nondegenerate bimatrix games

In two-person games where each player has a finite number of pure strategies, the set of Nash equilibria is a finite set when a certain nondegeneracy condition is satisfied. Recent investigations have shown that for n x n games, the cardinality of this finite set is bounded from above by a function phi(n) with 2(n) - 1 less than or equal to phi(n) less than or equal to (27/4)(n/2) - 1, where n is the maximal number of pure strategies of any player. In the present paper, we generalize this result to a class of games which may not satisfy the nondegeneracy condition. The set of Nash equilibria may be infinite; it is shown that it consists of no more than phi(n) are-connected components.