Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm

摘要

Stackelberg games are a classic example of bilevel optimization problems,which are often encountered in game theory and economics. These are complexproblems with a hierarchical structure, where one optimization task is nestedwithin the other. Despite a number of studies on handling bilevel optimizationproblems, these problems still remain a challenging territory, and existingmethodologies are able to handle only simple problems with few variables underassumptions of continuity and differentiability. In this paper, we consider aspecial case of a multi-period multi-leader-follower Stackelberg competitionmodel with non-linear cost and demand functions and discrete productionvariables. The model has potential applications, for instance in aircraftmanufacturing industry, which is an oligopoly where a few giant firms enjoy atremendous commitment power over the other smaller players. We solve cases withdifferent number of leaders and followers, and show how the entrance or exit ofa player affects the profits of the other players. In the presence of variousmodel complexities, we use a computationally intensive nested evolutionarystrategy to find an optimal solution for the model. The strategy is evaluatedon a test-suite of bilevel problems, and it has been shown that the method issuccessful in handling difficult bilevel problems.