An n-person noncooperative discounted vector valued dynamic game with a stopped set
The authors consider an n-person noncooperative dynamic game in which the payoff for each player is vector-valued. They define a domination relation between such vector payoffs by means of a convex cone D (i.e. one vector dominates another if their difference belongs to the cone). A D-convex noncooperative equilibrium is a strategy combination such that each player's payoff vector is undominated among all payoff vectors which this player could achieve, given the strategies of the other players. Under certain assumptions, they show the existence of such an equilibrium. Further, from a game with vector payoffs they construct a game with scalar payoffs by aggregating each player's vector payoff by means of weights. An equilibrium of this modified game yields a D-convex equilibrium of the original vector-valued game. Conversely, under some additional assumptions, every D-convex equilibrium of the original game yields an equilibrium for the modified (scalar) game, for suitably chosen weights.
scientific article; zbMATH DE number 4016634