Market exit and minimax regret

We study an overcrowded duopoly market where the only strategic variable is the exit time. We suppose that the surviving firm gets a positive monopoly profit and we focus on the classic context with complete information and identical firms. The only symmetric Nash equilibrium of this war of attrition is a mixed-strategy equilibrium that leads to a null expected payoff, i.e. the payoff a firm gets when it immediately exits the market. This result is not persuasive, both from an economic and from a strategic viewpoint. We argue that the minimax regret approach, that builds upon two opposite regrets - exiting the market too late and exiting the market too early - is more convincing. The minimax regret behavior, quite different from the mixed- strategy Nash equilibrium behavior, allows both firms to get a positive expected payoff.