A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes
This note demonstrates that a lattice game with strategic substitutes is dominancesolvable 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 Robertsâ€™ (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 outcomecompetition.
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Volume (Year): 36 (2007)
Issue (Month): 1 (September)
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- Vives, X., 1988.
"Nash Equilibrium With Strategic Complementarities,"
UFAE and IAE Working Papers
107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Bernheim, B Douglas, 1984.
"Rationalizable Strategic Behavior,"
Econometric Society, vol. 52(4), pages 1007-28, July.
- Vives, Xavier, 2004. "Complementarities and Games: New Developments," CEPR Discussion Papers 4742, C.E.P.R. Discussion Papers.
- Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
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