Equilibrium characterization and shock propagation in conflict networks

We establish the general properties of equilibria (existence and uniqueness) in a very general model of interconnected multiplayer conflicts. In particular, under mild conditions on the cost function and the contest technology, we show that a pure-strategy Nash equilibrium always exists and the set of Nash equilibria is convex. Furthermore, under the strong monotonicity of the cost function, the equilibrium is unique, regardless of the conflict structure. To establish these properties of equilibria, we use variational inequality techniques to obtain equivalent equilibrium characterizations. After conducting comparative statics analysis with respect to the model primitives, we explore, in several simple examples of conflict structures, how shocks that originated locally propagate to the rest of the conflict network. Our general framework subsumes a number of models studied in the contest literature, as we are able to generalize many results obtained in these papers.