Publication Type

Journal Article

Version

acceptedVersion

Publication Date

9-2020

Abstract

This paper introduces a novel concept of orders on types by which the so-called monotone comparative statics is valid in all supermodular games with incomplete information. We fully characterize this order in terms of what we call common optimism, providing a sense in which our order has a sharp epistemic interpretation. We say that type ti′ is higher than type ti in the order of the common optimism if ti′ is more optimistic about state than ti; ti′ is more optimistic that all players are more optimistic about state than ti; and so on, ad infinitum. First, we show that whenever the common optimism holds, monotone comparative statics hold in all supermodular games. Second, we show the converse. We construct an “optimism-elicitation game” as a single supermodular game with the property that whenever the common optimism fails, monotone comparative statics fails as well.

Keywords

common certainty of optimism, least equilibrium, greatest equilibrium, interim correlated rationalizaibility, monotone comparative statics, supermodularity, universal type space.

Discipline

Economic Theory

Research Areas

Economic Theory

Publication

Journal of Economic Theory

Volume

189

First Page

1

Last Page

33

ISSN

0022-0531

Identifier

10.1016/j.jet.2020.105082

Publisher

Elsevier

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.jet.2020.105082

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