2005•RePEc: Research Papers in EconomicsRequires access

A fixed point characterization of the dominancesolvability of lattice games with strategic substitutes

Alexander Zimper

Abstract

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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Key concepts: Mathematical economics, Strategic complements, Mathematics, Nash equilibrium, Cournot competition, Existential quantification, Lattice (music), Characterization (materials science)