Equilibrium strategies via GA to stackelberg games under multiple follower's best reply

Abstract

In this paper, we study a two-person game between one leader and one follower, called the Stackelberg game. The leader player enounces a decision before the others, and the follower takes into account this decision and solves an optimization problem that may have multiple solutions. Then, the leader optimizes his objective by assuming a given follower's reaction depending on his behavior. We consider in this paper a hierarchical equilibrium solution for a two-level game, particularly the strong Stackelberg solutions that corresponds to an optimistic leader's point of view and we give a numerical procedure based on a genetic algorithm (GA) evolution process to compute them. The use of a multimodal genetic algorithm allows us to approach the possible multiple solutions to the lower level problem. The algorithm convergence is illustrated by means of some test cases. © 2011 Wiley Periodicals, Inc.

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