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Unique equilibrium in contests with incomplete information


Ewerhart, Christian; Quartieri, Federico (2018). Unique equilibrium in contests with incomplete information. Working paper series / Department of Economics 133, University of Zurich.

Abstract

Considered are imperfectly discriminating contests in which players may possess private information about the primitives of the game, such as the contest technology, valuations of the prize, cost functions, and budget constraints. We find general conditions under which a given contest of incomplete information admits a unique pure-strategy Nash equilibrium. In particular, provided that all players have positive budgets in all states of the world, existence requires only the usual concavity and convexity assumptions. Information structures that satisfy our conditions for uniqueness include independent private valuations, correlated private values, pure common values, and examples of interdependent valuations. The results allow dealing with inactive types, asymmetric equilibria, population uncertainty, and the possibility of resale. It is also shown that any player that is active with positive probability ends up with a positive net rent.

Abstract

Considered are imperfectly discriminating contests in which players may possess private information about the primitives of the game, such as the contest technology, valuations of the prize, cost functions, and budget constraints. We find general conditions under which a given contest of incomplete information admits a unique pure-strategy Nash equilibrium. In particular, provided that all players have positive budgets in all states of the world, existence requires only the usual concavity and convexity assumptions. Information structures that satisfy our conditions for uniqueness include independent private valuations, correlated private values, pure common values, and examples of interdependent valuations. The results allow dealing with inactive types, asymmetric equilibria, population uncertainty, and the possibility of resale. It is also shown that any player that is active with positive probability ends up with a positive net rent.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C72, D23, D72, D82
Uncontrolled Keywords:Imperfectly discriminating contests, private information, existence and uniqueness of equilibrium, budget constraints, rent dissipation, Nash-Gleichgewicht, Vollkommene Information, Unvollkommene Information, Entscheidung bei Unsicherheit, Wettbewerb, Gewinnspiel
Language:English
Date:November 2018
Deposited On:27 Nov 2013 13:47
Last Modified:14 Nov 2018 14:23
Series Name:Working paper series / Department of Economics
Number of Pages:41
ISSN:1664-7041
Additional Information:Revised version ; former title: "Unique equilibrium in incomplete information contests with budget constraints"
OA Status:Green
Official URL:http://www.econ.uzh.ch/static/workingpapers.php?id=812

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