A model of a multilateral proxy war with spillovers
Economics, Finance and Quantitative Analysis
Motivated by the war in Syria and the ascension of ISIS, this paper models a proxy war with three sponsors and three combatants as a dynamic game. Sponsors are leaders that provide resources for combatants to fight each other. Sponsors 1 and 2 have strong aversion to sponsor 3’s proxy, but not against each other. Three pure strategy equilibria exist in the game. When the ex post value of winning is small, all players fight in equilibrium. However, when the ex post value of winning is large, in equilibrium either sponsors 1 and 2 coordinate their actions, with one of them staying out of the contest, or sponsor 3 does not participate. The probability of winning and the sponsors’ payoffs depend on a spillover effect. We find that no unique way of characterizing the comparative statics of the spillover effect emerges and that the answer varies from one equilibrium to another. Finally, we identify conditions under which sponsors 1 and 2 would want to form an alliance.
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