Abstract
This paper studies a class of multi-objective n-person non-zero sum games through a robust weighted approach where each player has more than one competing objective. This robust weighted multi-objective game model assumes that each player attaches a set of weights to its objectives instead of accessing accurate weights. Each player wishes to minimize its maximum weighted sum objective where the maximization is pointing to the set of weights. To address this new model, a new equilibrium concept-robust weighted Nash equilibrium is obtained. The existence of this new concept is proven on suitable assumptions about the multi-objective payoffs.
Highlights
This paper addresses the following multi-objective game with finite players in the normal form, MG: = (N, {Si}i 2 N, {Fi}i 2 N)
N: = {1, Á Á Á, n} is a finite set of players, Si & Rai is the set of actions for player i and Fi is the multi-objective payoff function of player i and the number of objectives is set as bi
We show that the robust weighted Nash equilibrium of MG inherits the properties of the weighted Nash equilibria, that is any robust weighted Nash equilibrium of MG with weights set Wi & Wri, i 2 N is either a weak Pareto equilibrium or a Pareto equilibrium
Summary
A weak Pareto optimal strategy) respectively to j2N;j61⁄4i the following multi-objective optimization, min FiðxÞ; xi 2Si ð1:1Þ that is there is no strategy ui 2 Si such that FiðxÀi; xiÞ " FiðxÀi; uiÞðresp: FiðxÀi; xiÞ 0 FiðxÀi; uiÞÞ; where the partial orders ≼ and 0 are defined as, for any given r, v 2 Rm, v 1 rðresp: v 0 rÞ()v À r 2 Rmþþ ðresp: r À v 2 RmþþÞ v # rðresp: v " rÞ()v À r 2 Rmþand r 61⁄4 vðresp: r À v 2 Rmþand r 61⁄4 vÞ: MG is a generalization of the scalar criterion games and is used to modelling situations where two or more decision makers, called players, take actions by considering their individual multiple objectives. If each player under an MG chooses the robust weighted approach, we show that there is at least a robust weighted Nash equilibrium which further guarantees the existence of the Pareto Nash equilibrium As such that the primary contributions of this paper are as follows. We prove the existence of a robust weighted Nash equilibrium
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
