The Min-Max Type Stackelberg Strategy for the Multi-Objective Problem and Its Application to the Multi-Objective Resource Allocation Problem

We consider the Stackelberg problem composed of a single leader and several followers which are interacting but cooperative mutually. Then the followers choose an unique solution from the noninferior solution set of the multi-objective optimization problem by mutual agreement. On the other hand, under uncertainties regarding the followers' agreement, the leader makes an optimal decision against the case where the worst noninferior solution for leader's objective function might be chosen from the noninferior solution set of the followers. That is to say, let the leader adopt the min-max criterion.In this paper, we call such a decision “the min-max type Stackelberg strategy for the multiple objective problem”, and the problem solving such a decision is formulated. And then, in the case where the min-max type Stackelberg strategy is adopted in the multiple objective resource allocation problem, we propose an algorithm to obtain the strategy as the optimal resource allocation.