A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models^†

Pareto optimality and Nash equilibrium are two standard solution concepts for cooperative and non-cooperative games, respectively. At the outset, these concepts are incompatible-see, for instance, [ 7 ] or [ 10 ]. But, on the other hand, there are particular games in which Nash equilibria turn out to be Pareto-optimal [ 1 ], [ 4 ], [ 6 ], [ 18 ], [ 20 ]. A class of these games has been identified in the context of discrete-time potential games [ 13 ]. In this paper we introduce several classes of deterministic and stochastic potential differential games [ 12 ] in which open-loop Nash equilibria are also Pareto optimal.