Abstract
In this paper, we propose a worst-case weighted approach to the multi-objective n-person non-zero sum game model where each player has more than one competing objective. Our “worst-case weighted multi-objective game” model supposes that each player has a set of weights to its objectives and wishes to minimize its maximum weighted sum objectives where the maximization is with respect to the set of weights. This new model gives rise to a new Pareto Nash equilibrium concept, which we call “robust-weighted Nash equilibrium”. We prove that the robust-weighted Nash equilibria are guaranteed to exist even when the weight sets are unbounded. For the worst-case weighted multi-objective game with the weight sets of players all given as polytope, we show that a robust-weighted Nash equilibrium can be obtained by solving a mathematical program with equilibrium constraints (MPEC). For an application, we illustrate the usefulness of the worst-case weighted multi-objective game to a supply chain risk management problem under demand uncertainty. By the comparison with the existed weighted approach, we show that our method is more robust and can be more efficiently used for the real-world applications.
Highlights
Multi-objective game is a generalization of the scalar criterion game and is used to model situations where two or more decision makers, called players, take actions by considering their individual multiple objectives
The computation for such an equilibrium, with the choice of polytope weight set for each player, is reformulated as a solution to a mathematical program with equilibrium constraints (MPEC) which can be solved by the existed methods (for example the sequential quadratic programming (SQP) methods)
We show that a robust weighted Nash equilibrium point can be calculated by solving a MPEC when the weight sets chosen by the players are polytopes
Summary
Multi-objective game is a generalization of the scalar criterion game and is used to model situations where two or more decision makers, called players, take actions by considering their individual multiple objectives. We consider n-person worst-case weighted multi-objective games where each player has two or more objectives and is ambiguous about the weights to the objectives. If each player in multi-objective games chooses the worst-case weighted approach, we show that there is at least a robust weighted Nash equilibrium which further guarantees the existence of the Pareto Nash equilibrium. The computation for such an equilibrium, with the choice of polytope weight set for each player, is reformulated as a solution to a mathematical program with equilibrium constraints (MPEC) which can be solved by the existed methods (for example the sequential quadratic programming (SQP) methods). Each retailer has more than one objectives to be considered and the corresponding robust weighted Nash equilibrium can be obtained by utilizing the proposed method in this paper
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.
