How to Select a Dual Nash Equilibrium

The paper analyzes situations, generalizing the duopoly problem, where two identical players are allowed with two control variables each, all of them linked through two non-strategic private constraints. Four dual equilibria are then obtained when each agent selects one leading variable to optimize and adjusts the other, and these equilibria are compared in a meta-game. For a simplified class of continuous games with linear constraints, it is shown that one symmetric dual equilibrium dominates the others and is the only perfect equilibrium of the metagame. The latter result holds locally for all quasi-concave utility functions and globally for all homogeneous ones, always keeping linear constraints. However, it is no longer valid in discrete games where the implicit constraints are not linear. Journal of Economic Literature Classification Numbers: C72, D43.