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A model of a multilateral proxy war with spillovers

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Abstract

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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Notes

  1. On terrorist spectaculars, see Arce (2010), Hoffman (2006) and Enders and Sandler (2012).

  2. On the growth of Islamic terrorism, see Enders and Sandler (2000) and Barros and Proena (2005).

  3. On ISIS, see Wood (2015).

  4. For an estimate of the economic impact of terrorism and conflicts on income per capita growth, see Gaibulloev and Sandler (2009). For the macroeconomic impacts of terrorism, see Blomberg et al. (2004) and Tavares (2004).

  5. Phares (2005) discusses the information war on Jihadism in academia and media, wherein Jihadists and their supporters actively participate, attempting to divert it, camouflage it, and move it in different directions.

  6. On conflict in dual population lands, see Levy and Faria (2007).

  7. For studies on armed groups switching sides during civil wars see Staniland (2012) and Otto (2017).

  8. A microeconomic study by Collier and Duponchel (2013) shows that during conflict, violence affects production through a form of technical regress and demand through a reduction in income. For an overview of disaggregated studies and the micro-dynamics of individual civil wars, see Cederman and Gleditsch (2009).

  9. Sorli et al.’s (2005) study of Middle East conflict finds ethnic dominance to be a significant determinant of violence. In addition, the authors find that economic development and economic growth, in addition to longer periods of peace, generally reduce the likelihood of conflict.

  10. Bevi and Corchon (2010) examine a complete information war game in which the initial distribution of resources is heterogeneous.

  11. For surveys of contest games, see Corchon (2007) and Corchon and Serena (2018).

  12. Katz et al. (1990) analyze group contests wherein groups vary in their numbers of members. They find that when the members are identical, all groups exert the same aggregate effort regardless of asymmetries in group size.

  13. It has been alleged that ISIS also has state sponsors, but to the best of our knowledge that conjecture has not been established clearly. We therefore avoid that issue.

  14. In that case, it is assumed that \(s_{1}\) and \(s_{2}\) do not provide any resources to the combatants.

  15. For details, see the Online Appendix.

  16. Following Sanchez-Pages (2007), we do not explicitly discuss the division of the alliance’s payoff among its individual constituents. However, one way to divide the aggregate payoff is to pay each constituent an amount equal to the outside option plus a fraction of the leftover surplus.

  17. We show this ratio since it is independent of V and t.

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Authors and Affiliations

  1. Department of Economics, Kennesaw State University, Kennesaw, GA, 30144, USA

    Aniruddha Bagchi & Timothy Mathews

  2. Department of Economics, Florida Atlantic University, Boca Raton, FL, 33431, USA

    João Ricardo Faria

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  1. Aniruddha Bagchi
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Correspondence to Aniruddha Bagchi.

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Bagchi, A., Faria, J.R. & Mathews, T. A model of a multilateral proxy war with spillovers. Public Choice 179, 229–248 (2019). https://doi.org/10.1007/s11127-018-0586-5

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