Abstract
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.
Highlights
Pareto efficiency and Nash equilibrium are two standard solution concepts for cooperative and non-cooperative games, respectively
Our main objective is to identify some classes of potential differential games (PDGs) which have Nash equilibria that are a Pareto solution
In this note we have identified several classes of openloop differential games, for both deterministic and stochastic models, which have open-loop Pareto-optimal Nash equilibria
Summary
Pareto efficiency and Nash equilibrium are two standard solution concepts for cooperative and non-cooperative games, respectively. Assuming that the players want to maximize their payoff functions, a Nash equilibrium for the game (1)-(2) is defined as a multistrategy u∗ such that. From [12], if (1)-(2) is a PDG with an associated OCP as in Remark 1, P is called a potential function for the game. 3. Differential games with Pareto-optimal Nash equilibria. The simplest example of a PDG with Pareto-optimal Nash equilibria is a team game, defined as follows. (As noted in [12], a team game can have a Nash equilibrium that is not an optimal solution for the associated OCP.). The associated OCP has a unique optimal solution, which is an open-loop Nash equilibrium for the game (7)-(8) (see example 3 in [12]).
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