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A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes

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Abstract

We demonstrate that a lattice game with strategic substitutes is dominance-solvable if and only if there exists a unique fixed point of the function that results from an iteration of the best response function. This finding complements a result of Milgrom and Roberts’ (Econometrica 58:1255–1277, 1990) by which a lattice game with strategic complements is dominance-solvable if and only if there exists a unique Nash equilibrium. We illustrate our main result by an application to a model of Cournot outcome-competition.

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Authors and Affiliations

  1. School of Economics, University of Cape Town, Private Bag, Rondebosch, 7701, Cape Town, South Africa

    Alexander Zimper

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  1. Alexander Zimper
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Correspondence to Alexander Zimper.

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Zimper, A. A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes. Int J Game Theory 36, 107–117 (2007). https://doi.org/10.1007/s00182-007-0073-6

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  • DOI: https://doi.org/10.1007/s00182-007-0073-6

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