Context: I would like to know how likely a player is to pick a specific action, provided that he plays optimally and the action is optimal. Phrased like this, the question is ill-defined. But is there some way around the problem?
Details: I have a zero-sum symmetric matrix game. Is there some good notion of a Nash equilibrium with a maximum support [edit: maximum among the NE strategies]? Like something along the lines of "take the center of the simplex of NE strategies"?
The question: Is there some canonical solution to the vague question above? Possibly something already written down in a textbook or a paper. (It would feel silly to reinvent the wheel.)