Regular Equilibria and Negative Welfare Implications in Delegation Games

This study examines delegation games in which each player commits to a reaction function in advance. We focus on the regular subgame perfect equilibria of delegation games in the sense that the chosen reaction functions have an invertible Jacobian. Subsequently we provide a necessary condition under which an action profile is achieved as a regular equilibrium of n-player delegation games. In two-player games with misaligned preferences, each efficient action profile violates the necessary condition. We also show that almost action profiles other than efficient ones are achieved as regular equilibria of the delegation game in which the chosen reaction functions are linear. This finding implies that each delegatee’s objective is written as a quadratic function, which may justify the linear-quadratic specification of the objective functions in applications.