Constrained multiobjective games in general topological space
type: Item
instance of: scholarly article
title: Constrained multiobjective games in general topological space
zbMATH Open document ID: 0963.91013
DOI: 10.1016/S0898-1221(99)00330-2
author: Xieping Ding
publication date: 2000-09-20T00:00:00Z
review text: 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.
reviewed by: Srinivas Raghava Mohan
Mathematics Subject Classification ID: 91A20
Mathematics Subject Classification ID: 91A44
Mathematics Subject Classification ID: 91A06
zbMATH DE Number: 1471554
zbMATH Keywords: constrained multiobjective game
zbMATH Keywords: quasi-equilibrium problem
zbMATH Keywords: weighted Nash equilibria
zbMATH Keywords: Pareto equilibria
zbMATH Keywords: topological space
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1471554