Discussion Paper Details

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Title: Networks in Conflict: A Variational Inequality Approach

Author(s): Jin Xu, Yves Zenou and Junjie Zhou

Publication Date: April 2019

Keyword(s): Contests, network games and variational inequality

Programme Area(s): Public Economics

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.

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Bibliographic Reference

Xu, J, Zenou, Y and Zhou, J. 2019. 'Networks in Conflict: A Variational Inequality Approach'. London, Centre for Economic Policy Research.