Characterization of Markovian equilibria in a class of differential games

We consider an alternative method to the classical one for the determination of Markov perfect Nash equilibria. The approach shown in the paper is based on the study of a quasi-linear system of partial differential equations instead of the Hamilton–Jacobi–Bellman system. The simpler structure of the former allows us to determine existence and uniqueness of Nash equilibria in non-renewable resource games under some assumptions. When closed-form solutions are not available, we give a method to obtain numerical solutions.Financial support from Investigation Projects PB98-0393 of Direcci-on General de Ense˜nanza Superior e Investigaci-on Cient-XKca and VA 108/01 of Junta de Castilla y Le-on are gratefully acknowledged. The author is grateful to two anonymous referees for their comments and corrections. I am also indebted to the Associated Editor Tamer BaHsar for his remarks and for the careful reading of the manuscript. The author is responsible for any remaining error.Publicad