Pure Strategy Nash Bargaining Solutions

Abstract

A broad class of 2-person threat games for which a unique pure strategy Nash bargaining solution exists is characterized in terms of three, simple, empirically meaningful restrictions on the joint objective function: compact domain, continuity, and "corner concavity." Connectedness [in particular, convexity] of the strategy and payoff sets is not required. In addition, conditions are given for the existence of a pure strategy Nash equilibrium threat solution. Connectedness of the strategy and payoff sets is again not required.