Markov perfect equilibria in differential games with regime switching
Van Long , Ngo (McGill University, Montreal(Canada). Department of Economics) | Prieur , Fabien (INRA , Montpellier (France). UMR 1135 Laboratoire Montpelliérain d'Economie Théorique et Appliquée) | Puzon , Klarizze (Université Montpellier 1, Montpellier(France). Laboratoire Montpelliérain d'Economie Théorique et Appliquée, Montpellier) | Tidball , Mabel (INRA , Montpellier (France). UMR 1135 Laboratoire Montpelliérain d'Economie Théorique et Appliquée)
We propose a new methodology exploring Markov perfect equilibrium strategies in di erential games with regime switching. Speci cally, we develop a general game with two players having two kinds of strategies. Players choose an action that in uences the evolution of a state variable, and decide on the switching time between alternative and consecutive regimes. Compared to the optimal control problem with regime switching, necessary optimality conditions are modi ed for the rst-mover. When choosing her optimal switching strategy, this player considers her impact on the other player's actions and welfare, vice versa. In order to deter- mine the optimal timing between regime changes, the notion of erroneous timing is introduced and necessary conditions for a particular timing to be erroneous are derived. We then apply this original material to an ex- haustible resource extraction game. Sucient conditions for the existence of an interior solution are compared to those characterizing an erroneous timing. The impact of feedback strategies for adoption time on the equi- librium depends on con icting e ects: the rst mover incurs an indirect cost due to the future switching of her rival (incentive to delay the switch). But she is able to a ect the other player's switching decision (incentive to switch more rapidly). In a particular case with no direct switching cost, the interplay between the two ensures that the rst-mover adopts the new technology in nite time. Interestingly, this result di ers from what is obtained in a non-game theoretic framework, i.e. immediate adoption.
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