Finiteness and Inefficiency of Nash Equilibria,
Abstract
Our aim is to explore efficiency, as well as strongness, of the Nash Equilibria (N.E.) of finite-person noncooperative games in strategic form. We show that--with smooth strategy sets and payoff functions--it is almost always the case that the N.E. are finite in number; efficient N.E. are extremal points; and strong N.E. are inactive points. Extremal (inactive) points are points in the Cartesian product of the players' strategy sets at which at least one (at most one) of the players is (is not) at a 'vertex' of her/his strategy set. Both sets of points are therefore thin (they are nonexistent if the strategy-sets are vertex-free). This result is not very surprising because efficiency or strongness is generally an outcome of cooperation. And, indeed, it has been part of the folklore of Game Theory (witness: the Prisoners' Dilemma).
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 17, 1978
- Accession Number
- ADA063611
Entities
People
- Pradeep Dubey
Organizations
- Yale University