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Dynamics of Information Systems: Mathematical Foundations pp 267–280Cite as

A Hierarchical MultiModal Hybrid Stackelberg–Nash GA for a Leader with Multiple Followers Game

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 20))

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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Author information

Authors and Affiliations

  1. Dipartimento di Scienze Applicate, Università degli Studi di Napoli “Parthenope”, Centro Direzionale di Napoli, Isola C 4, 80143, Napoli, Italy

    Egidio D’Amato

  2. Dipartimento di Ingegneria Aerospaziale, Università degli Studi di Napoli “Federico II”, Via Claudio 21, 80125, Napoli, Italy

    Elia Daniele & Simone Tancredi

  3. Mechanical Engineering and Institute for Computational Mathematical Engineering, Stanford University, Building 500, Stanford, CA, 94305-3035, USA

    Giovanni Petrone

  4. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Claudio 21, 80125, Napoli, Italy

    Lina Mallozzi

Authors
  1. Egidio D’Amato
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  2. Elia Daniele
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  3. Lina Mallozzi
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  4. Giovanni Petrone
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  5. Simone Tancredi
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Corresponding author

Correspondence to Lina Mallozzi .

Editor information

Editors and Affiliations

  1. , Industrial and Systems Engineering, University of Florida, Weil Hall 303, Gainesville, 32611, Florida, USA

    Alexey Sorokin

  2. Munitions Directorate, AFRL, GNC Branch, W. Eglin Blvd 101, Eglin AFB, 32542, Florida, USA

    Robert Murphey

  3. Dept. Computer & Information Science &, Engineering (CISE), University of Florida, E450, CSE Building, Gainesville, 32611, Florida, USA

    My T. Thai

  4. , Department of Industrial and Systems Eng, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

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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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