Constrained multiobjective games in general topological space (Q1570118)

Multiobjective games are games in which the payoff to a player is a vector-valued function of the strategies. This paper introduces and studies a new class of constrained multiobjective games in which the set of strategies of the \(i\)-th player is a general topological space \(X^i.\) The set of feasible strategies for the \(i\)-th player is constrained to be a subset \(A^i(x^{\hat{i}})\) of \(X^i,\) given the remaining \((n-1)\) players' strategy choice \(x^i\in \prod _{j\neq i}X_j.\) Let \(x\in \prod _{i=1}^nX^i. \) The payoff to player \(i\) is a function \(F^i(x) = (f_1^i(x), f_2^i(x), \ldots ,f_{k_i}^i(x)):X\rightarrow R^{k_i}.\) Given such a game, the concepts of weighted Nash equilibrium and Pareto equilibrium can be defined and this paper proves the existence of such equilibria under certain assumptions.