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.
Equilibrium strategies via GA to Stackelberg games under multiple follower’s best reply
E. D'Amato;
2012-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
