Abstract
In this paper a numerical procedure based on a genetic algorithm (GA) evolution process is given to compute a Stackelberg solution for a hierarchical n + 1-person game. There is a leader player who enounces a decision before the others, and the rest of players (followers) take into account this decision and solve a Nash equilibrium problem. So there is a two-level game between the leader and the followers, called Stackelberg–Nash problem. The idea of the Stackelberg-GA is to bring together genetic algorithms and Stackelberg strategy in order to process a genetic algorithm to build the Stackelberg strategy. In the lower level, the followers make their decisions simultaneously at each step of the evolutionary process, playing a so called Nash game between themselves. The use of a multimodal genetic algorithm allows to find multiple Stackelberg strategies at the upper level. In this model the uniqueness of the Nash equilibrium at the lower-level problem has been supposed. The algorithm convergence is illustrated by means of several test cases.
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D’Amato, E., Daniele, E., Mallozzi, L., Petrone, G., Tancredi, S. (2012). A Hierarchical MultiModal Hybrid Stackelberg–Nash GA for a Leader with Multiple Followers Game. In: Sorokin, A., Murphey, R., Thai, M., Pardalos, P. (eds) Dynamics of Information Systems: Mathematical Foundations. Springer Proceedings in Mathematics & Statistics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3906-6_14
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DOI: https://doi.org/10.1007/978-1-4614-3906-6_14
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