Monotone equilibria in Bayesian games of strategic complementarities

doi:10.1016/j.jet.2006.02.009

Journal of Economic Theory

Volume 134, Issue 1, May 2007, Pages 339-360

https://doi.org/10.1016/j.jet.2006.02.009 Get rights and content

Abstract

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayesian Nash equilibrium, each one in strategies that are monotone in type. Our main assumptions, besides strategic complementarities, are that each player's payoff displays increasing differences in own action and the profile of types and that each player's interim beliefs are increasing in type with respect to first-order stochastic dominance (e.g., types are affiliated). The result holds for general action and type spaces (single-, multi-, or infinite-dimensional; continuous or discrete) and no prior is assumed. We also provide the following comparative statics result: the greatest and least equilibria are higher if there is a first-order stochastic dominant shift in the interim beliefs. We apply this result to strategic information revelation in games of voluntary disclosure.

References (32)

A.S. Edlin et al.
Strict monotonicity in comparative statics
J. Econ. Theory
(1998)
D.M. Frankel et al.
Equilibrium selection in global games with strategic complementarities
J. Econ. Theory
(2003)
X. Vives
Nash equilibrium with strategic complementarities
J. Math. Econ.
(1990)
S. Athey, Characterizing Properties of Stochastic Objective Functions, MIT and NBER,...
S. Athey
Single crossing properties and the existence of pure strategy equilibria in games of incomplete information
Econometrica
(2001)
S. Athey
Monotone comparative statics under uncertainty
Quart. J. Econ.
(2002)
R. Aumann et al.
Approximate purification of mixed strategies
Mathematics Operations Res.
(1982)
H. Carlsson et al.
Equilibrium selection in global games with strategic complementarities
Econometrica
(1993)
R. Cooper et al.
Coordinating coordination failures in keynesian models
Quart. J. Econ.
(1988)
C. Dellacherie et al.
Probabilities and Potential
(1978)

D. Fudenberg et al.

Existence of Equilibrium in Large Double Auctions

(2005)

S. Grossman

The informational role of warranties and private disclosure about the product quality

J. Law Econ.

(1981)

J. Hadar et al.

Application in economic theory and analysis

J. Harsanyi et al.

A General Theory of Equilibrium Selection in Games

(1988)

B. Lebrun

Existence of an equilibrium in first-price auctions

Econ. Theory

(1996)

E. Maskin et al.

Equilibrium in sealed high bid auctions

Rev. Econ. Stud.

(2000)

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Monotone equilibria in Bayesian games of strategic complementarities

Abstract

J. Econ. Theory

J. Econ. Theory

J. Math. Econ.

Single crossing properties and the existence of pure strategy equilibria in games of incomplete information

Econometrica

Monotone comparative statics under uncertainty

Quart. J. Econ.

Approximate purification of mixed strategies

Mathematics Operations Res.

Equilibrium selection in global games with strategic complementarities