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Formalization Of Multi-Level Games

Author

Listed:
  • KJELL HAUSKEN

    (School of Economics, Culture and Social Sciences, University of Stavanger, N-4068 Stavanger, Norway)

  • ROSS CRESSMAN

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada)

Abstract

The article presents multilevel game theory, as a generalization of conventional single-level game theory as it has developed since von Neumann and Morgenstern (1944). We define a multilevel game structure, multilevel games, payoffs and distribution rules, upward feasible strategies and the solution concept multilevel Nash equilibrium (MNE) in such games. A MNE must be, for each player, a best reply against itself with respect to alternative strategies that may have other players deviate as well, in contrast to the NE for conventional games where simultaneous deviations by more than one player are not considered. Although every pure or mixed MNE must give the same outcome as a NE of the extensive form representation, a NE is not necessarily a MNE. It is shown that a MNE need not exist in pure or mixed strategies and, if it does, it may not be unique. In the former case, the multilevel structure is considered unmaintainable.

Suggested Citation

  • Kjell Hausken & Ross Cressman, 2004. "Formalization Of Multi-Level Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 195-221.
  • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:02:n:s0219198904000150
    DOI: 10.1142/S0219198904000150
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    References listed on IDEAS

    as
    1. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Anna Gunnthorsdottir & Palmar Thorsteinsson, 2024. "Productivity or privilege - Game-theoretic and experimental models of social class," Economics wp98, Department of Economics, Central bank of Iceland.
    2. Hausken, Kjell, 2006. "Jack Hirshleifer: A Nobel Prize left unbestowed," European Journal of Political Economy, Elsevier, vol. 22(2), pages 251-276, June.
    3. Fenling Feng & Chengguang Liu & Jiaqi Zhang, 2020. "China's Railway Transportation Safety Regulation System Based on Evolutionary Game Theory and System Dynamics," Risk Analysis, John Wiley & Sons, vol. 40(10), pages 1944-1966, October.
    4. Tverskoi, Denis & Senthilnathan, Athmanathan & Gavrilets, Sergey, 2021. "The dynamics of cooperation, power, and inequality in a group-structured society," SocArXiv 24svr_v1, Center for Open Science.
    5. Tverskoi, Denis & Senthilnathan, Athmanathan & Gavrilets, Sergey, 2021. "The dynamics of cooperation, power, and inequality in a group-structured society," SocArXiv 24svr, Center for Open Science.
    6. Kjell Hausken, 2016. "Gordon Tullock: A Nobel Prize left unbestowed," Journal of Bioeconomics, Springer, vol. 18(2), pages 121-127, July.

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    More about this item

    Keywords

    Multilevel game theory; methodological individualism; empowerment from below; multilevel Nash equilibrium; JEL Classification Number C79;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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