Big Dog’s Dilemma: Feint Equilibrium

How can an underdog defend its territory against a bigger dog’s threat? Feint can be implemented. We will define a new equilibrium: Feint equilibrium. When an action set of the dogs is continuous, the equilibrium is well-defined. In the equilibrium, the dogs make less extreme choices than in Perfect Bayesian equilibrium. We have found the more interesting result that behavioral type of the big dog actually determines final outcome when the action set of the dogs is discrete. A risk-averse big dog quits the confrontation because the dog feels that possibility of feint deepens unpredictability of the game. This paper can contribute to the literature of signaling game, dynamic interaction and firm behavior.