Markov Perfect Equilibria in Differential Games with Regime Switching Strategies

We propose a new methodology exploring Markov perfect equilibrium strategies in differential games with regime switching. Specifically, we develop a general game with two players having two kinds of strategies. Players choose an action that inuences the evolution of a state variable, and decide on the switching time from one regime to another. Compared to the optimal control problem with regime switching, necessary optimaliity conditions are modified for the first-mover. When choosing her optimal switching strategy, this player considers the impact of her choice on the other player's actions and payoffs. In order to determine the equilibrium timing of regime changes, the notion of wrong timing is introduced and necessary conditions for a particular timing to be wrong are derived.[...]