Differential Games with (A) symmetric Players and Heterogeneous Strategies

Abstract

One family of heterogeneous strategies in differential games with (a)symmetric players is developed in which one player adopts an anticipating open-loop strategy and the other adopts a standard Markovian strategy. Via conjecturing principle, the anticipating open-loop strategic player plans her strategy based on the possible updating the rival player may take. These asymmetric strategies should be appropriate choices in some modelling circumstances and they frame one of the infinitely many non-degenerate Markovian Nash Equilibrium. Except the stationary path, this kind of strategy makes the study of short-run trajectory possible, which usually are not subgame perfect. However, the short-run non-perfection may provide very important policy suggestions.