The Existence and Uniqueness of Monotone Pure Strategy Equilibrium in Bayesian Games

Robin Mason and Akos Valentinyi ()

Discussion Paper Series In Economics And Econometrics from University of Southampton, Economics Division, School of Social Sciences

Abstract: This paper provides a sufficient condition for existence and uniqueness of equilibrium, which is in monotone pure strategies, in a broad class of Bayesian games. The argument requires that the incremental interim payoff - the expected payoff difference between any two actions, conditional on a player's realised type - satisfies two conditions. The first is uniform strict single-crossing with respect to own type. The second condition is Lipschitz continuity with respect to opponents' strategies. Our main result shows that, if these two conditions are satisfied, and the bounding parameters satisfy a particular inequality, then the best response correspondence is a contraction, and hence there is a unique equilibrium of the Bayesian game. Furthermore, this equilibrium is in monotone pure strategies. We characterize the uniform monotonicity and Lipschitz continuity conditions in terms of the model primitives. We also consider a number of examples to illustrate how the approach can be used in applications.

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:stn:sotoec:0710

Access Statistics for this paper

More papers in Discussion Paper Series In Economics And Econometrics from University of Southampton, Economics Division, School of Social Sciences
Contact information at EDIRC.
Series data maintained by Chris Thorn ().