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High-Dimensional Nash Equilibria Problems and Tensors Applications

Author

Listed:
  • J. E. Abdou

    (Faculty of Economics and Business Administration, Lebanese University, Beirut, Lebanon)

  • E. Safatly

    (Faculty of Economics and Business Administration, Lebanese University, Beirut, Lebanon)

  • B. Nakhle

    (Faculty of Economics and Business Administration, Lebanese University, Beirut, Lebanon)

  • A. El Khoury

    (Faculty of Economics and Business Administration, Lebanese University, Beirut, Lebanon)

Abstract

We propose, in this work, an overview on tensors application in game theory, and basically on Nash equilibria problems. In this paper, we extend the classic normal form of a game to a new form called Tensor form. We present some tensors concepts and operations with detailed examples and then we propose an efficient methodology to solve pure and mixed high-dimensional Nash equilibria problems using tensors operations. The efficiency of this methodology is shown in numerical examples for pure and mixed strategy. An algorithm based on tensors is also implemented to describe and solve these problems.

Suggested Citation

  • J. E. Abdou & E. Safatly & B. Nakhle & A. El Khoury, 2017. "High-Dimensional Nash Equilibria Problems and Tensors Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-25, September.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500153
    DOI: 10.1142/S0219198917500153
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    References listed on IDEAS

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    1. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    3. J. Douglas Carroll & Sandra Pruzansky & Joseph Kruskal, 1980. "Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 3-24, March.
    4. Goldberg, Paul W. & Pastink, Arnoud, 2014. "On the communication complexity of approximate Nash equilibria," Games and Economic Behavior, Elsevier, vol. 85(C), pages 19-31.
    5. Cobb, Barry R. & Sen, Tinni, 2014. "Finding mixed strategy Nash equilibria with decision trees," International Review of Economics Education, Elsevier, vol. 15(C), pages 43-50.
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