Characterizing Pure Strategy Nash Equilibria in Finite Noncooperative Games

The classical existence result of Nash guarantees that every finite noncooperative game admits an equilibrium in mixed strategies, but it leaves open the question of when pure strategy equilibria exist.

This paper develops a structural approach to that question by exploiting properties of the best-response correspondence on finite strategy sets.

Building on recent work, we derive new sufficient conditions for the existence of pure strategy Nash equilibria in finite games.

We introduce several broad classes of finite games for which pure equilibria are guaranteed, including a class that generalizes unilaterally competitive games and a class characterized by the existence of an aggregate-payoff maximizer over an ordered set.

Our results clarify the role of acyclicity, and aggregation in producing pure equilibria and connect disparate sufficient-condition results in the literature into a unified framework.