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Fall back equilibrium for $$2 \times n$$ bimatrix games

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  • John Kleppe
  • Peter Borm
  • Ruud Hendrickx

Abstract

In this paper we provide a characterization of the set of fall back equilibria for $$2 \times n$$ bimatrix games. Furthermore, for this type of games we discuss the relation between the set of fall back equilibria and the sets of perfect, proper and strictly perfect equilibria. In order to do this we reformulate the existing characterizations for these three equilibrium concepts by the use of refinement-specific subgames. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • John Kleppe & Peter Borm & Ruud Hendrickx, 2013. "Fall back equilibrium for $$2 \times n$$ bimatrix games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 171-186, October.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:2:p:171-186
    DOI: 10.1007/s00186-013-0438-5
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    References listed on IDEAS

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    1. Kleppe, J. & Borm, P.E.M. & Hendrickx, R.L.P., 2012. "A Strategic Foundation for Proper Equilibrium," Discussion Paper 2012-093, Tilburg University, Center for Economic Research.
    2. Kleppe, John & Borm, Peter & Hendrickx, Ruud, 2012. "Fall back equilibrium," European Journal of Operational Research, Elsevier, vol. 223(2), pages 372-379.
    3. Borm, P.E.M. & Jansen, M.J.M. & Potters, J.A.M. & Tijs, S.H., 1993. "On the structure of the set of perfect equilibria in bimatrix games," Other publications TiSEM 5a4170b8-1cb6-416f-b944-e, Tilburg University, School of Economics and Management.
    4. Borm, P.E.M. & Gijsberts, A. & Tijs, S.H., 1989. "A geometric-combinatorial approach to bimatrix games," Other publications TiSEM af7a280a-3e50-4bdf-b537-8, Tilburg University, School of Economics and Management.
    5. Borm, P.E.M., 1992. "On perfectness concepts for bimatrix games," Other publications TiSEM 9652c2b4-b09f-4c05-846a-3, Tilburg University, School of Economics and Management.
    6. Jansen, Mathijs, 1993. "On the Set of Proper Equilibria of a Bimatrix Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(2), pages 97-106.
    7. Rangan A & Kalro A H, 1974. "Stochastic Models for Stock Price Fluctuations," IIMA Working Papers WP1974-09-01_00129, Indian Institute of Management Ahmedabad, Research and Publication Department.
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    Cited by:

    1. John Kleppe & Peter Borm & Ruud Hendrickx, 2017. "Fall back proper equilibrium," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 402-412, July.

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    More about this item

    Keywords

    Game theory; Fall back equilibrium; $$2 times n$$ bimatrix game; Equilibrium refinement; C72;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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