Weak Monotone Comparative Statics
63 Pages Posted: 12 Dec 2019
Date Written: November 14, 2019
We develop a theory of monotone comparative statics based on weak set order, or in short weak monotone comparative statics, and identify the enabling conditions in the context of individual choices, Pareto optimal choices for a coalition of agents, and Nash equilibria of games. Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environment and underlying preferences of agents. We apply the theory to establish existence and monotone comparative statics of Nash equilibria in games with strategic complementarities and of stable many-to-one matchings in two-sided matching problems, allowing for general preferences that accommodate indifferences and incomplete preferences.
Keywords: monotone comparative statics, weak set order, fixed-point theorem, games with strategic complementarities, stable two-sided many-to-one matchings
JEL Classification: C61, C72, D47
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