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Rationalizability, adaptive dynamics, and the correspondence principle in games with strategic substitutes

Published: 14 May 2010 Publication History

Abstract

New insights into the theory of games with strategic substitutes (GSS) are developed. These games possess extremal serially undominated strategies that provide bounds on predicted behavior and on limiting behavior of adaptive dynamics, similar to games with strategic complements (GSC). In parameterized GSS, monotone equilibrium selections are dynamically stable under natural conditions, as in parameterized GSC. Dominance solvability in GSS is not equivalent to uniqueness of Nash equilibrium, but is equivalent to uniqueness of simply rationalizable strategies. Convergence of best response dynamics in GSS is equivalent to global convergence of adaptive dynamics, is equivalent to dominance solvability, and implies uniqueness of equilibrium, all in contrast to GSC. In particular, Cournot stability is equivalent to dominance solvability in GSS. The results shed light on predicted behavior, learning, global stability, uniqueness of equilibrium, and dynamic stability of monotone comparative statics in GSS. Several examples are provided.

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  1. Rationalizability, adaptive dynamics, and the correspondence principle in games with strategic substitutes

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    BQGT '10: Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions
    May 2010
    155 pages
    ISBN:9781605589190
    DOI:10.1145/1807406
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    Published: 14 May 2010

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