Networks in Conflict: A Variational Inequality Approach

51 Pages Posted: 25 Apr 2019

See all articles by Jin Xu

Jin Xu

Shandong University

Yves Zenou

Monash University - Department of Economics; Stockholm University; Research Institute of Industrial Economics (IUI); IZA Institute of Labor Economics; Centre for Economic Policy Research (CEPR)

Junjie Zhou

National University of Singapore (NUS), Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: April 2, 2019

Abstract

We study a very general contest game in which players exert efforts in multiple battles. The conflict structure, which represents who participates in which battlefield, is arbitrary and can be represented by a hypergraph. We show, under mild conditions on the cost function and contest technology, that the set of pure strategy Nash equilibria is nonempty and convex, and provide equivalent characterizations using techniques from Variational Inequality (VI). We demonstrate that the strong monotonicity of the cost function always implies the uniqueness of Nash equilibrium regardless of the conflict structure. We also perform an extensive comparative statics analysis with respect to the parameters of the model and discuss several applications of our model. Our general model incorporates many existing models of single or multi-battle contests as special cases when the conflict network and/or the cost function take particular forms.

Keywords: network games, multi-battle contests, variational inequality, uniqueness, comparative statics

JEL Classification: C72, D74, D85

Suggested Citation

Xu, Jin and Zenou, Yves and Zhou, Junjie, Networks in Conflict: A Variational Inequality Approach (April 2, 2019). Available at SSRN: https://ssrn.com/abstract=3364087 or http://dx.doi.org/10.2139/ssrn.3364087

Jin Xu

Shandong University ( email )

27 Shanda Nanlu
South Rd.
Jinan, Shandong 250100
China

Yves Zenou (Contact Author)

Monash University - Department of Economics ( email )

Australia

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Research Institute of Industrial Economics (IUI) ( email )

P.O. Box 5501
S-114 85 Stockholm
Sweden

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Junjie Zhou

National University of Singapore (NUS), Department of Economics ( email )

Singapore
Singapore

HOME PAGE: http://zhoujunjie.weebly.com/

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