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Fall back equilibrium for \(2 \times n\) bimatrix games

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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.

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Notes

  1. A strategy \(q \in \Delta _N\) is dominated if there exists a strategy \(\bar{q}\in \Delta _N\) such that \(pB\bar{q}\ge pBq\) for all \(p \in \Delta _M\) and \(pB\bar{q}>pBq\) for some \(p \in \Delta _M\).

  2. In Kleppe et al. (2012a) the notation \(PS\) is used for the set of pure secondary replies. However, to clearly distinguish between the set of pure solutions and the set of pure secondary replies, we use the notation \(\textit{PSR}\) for the latter in this paper.

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Authors and Affiliations

  1. Center and Department of Econometrics and Operations Research, Tilburg University, PO Box 90153, 5000 LE , Tilburg, The Netherlands

    John Kleppe & Peter Borm

  2. Center and Department of Organization and Strategy, Tilburg University, Tilburg, The Netherlands

    Ruud Hendrickx

Authors
  1. John Kleppe
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  2. Peter Borm
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  3. Ruud Hendrickx
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Correspondence to John Kleppe.

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Kleppe, J., Borm, P. & Hendrickx, R. Fall back equilibrium for \(2 \times n\) bimatrix games. Math Meth Oper Res 78, 171–186 (2013). https://doi.org/10.1007/s00186-013-0438-5

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  • DOI: https://doi.org/10.1007/s00186-013-0438-5

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