Costly Leader Games with a Probabilistically Non-Strategic Leader

Abstract

I consider a two-person costly leader game — in which the follower endogenously chooses whether to buy information about the leader, and a follow-up action — with a twist. With a known probability, the leader is a nonstrategic type. A strategic type leader may choose to masquerade as a nonstrategic type, at a cost. I show that, if the follower’s cost of information is not too large, and the probability of the leader being nonstrategic is neither too large nor too small, this game has no pure strategy equilibrium. Moreover, the equilibrium of the simultaneous-move complete information game is inaccessible as follower information cost converges to zero. There is no equilibrium outcome in which leader advantage is destroyed: however, a mixed strategy equilibrium exists which does preserve leader advantage in the sense that payoffs and strategies converge to those of the sequential-move complete information equilibrium as information cost tends to zero. My results differ from some traditional results in costly leader games, and are due to the interaction of two forces, the “type uncertainty” and the “money down the drain” effects. To my knowledge this is the first paper to integrate behavioral types into costly leader games (other papers considering heterogeneity in type do not consider nonstrategic players).