Working Paper: CEPR ID: DP13647
Authors: Jin Xu; Yves Zenou; Junjie Zhou
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; Contests; Variational Inequality
JEL Codes: C72; D74; D85
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| cost function (D24) | uniqueness of Nash equilibrium (C72) |
| strong monotonicity of cost function (D42) | uniqueness of Nash equilibrium (C72) |
| changes in battle valuations (D46) | equilibrium outcomes (D51) |
| changes in cost functions (D24) | equilibrium outcomes (D51) |
| structural properties of conflict network (D74) | multiplicity of equilibria (C62) |