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
On ISIS, see Wood (2015).
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.
On conflict in dual population lands, see Levy and Faria (2007).
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).
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.
Bevi and Corchon (2010) examine a complete information war game in which the initial distribution of resources is heterogeneous.
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.
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.
In that case, it is assumed that \(s_{1}\) and \(s_{2}\) do not provide any resources to the combatants.
For details, see the Online Appendix.
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.
We show this ratio since it is independent of V and t.
References
Anderton, C. H., & Carter, J. R. (2009). Principles of conflict economics. New York, NY: Cambridge University Press.
Arce, D. (2010). Terrorist spectaculars: Backlash attacks and the focus of intelligence. Journal of Conflict Resolution, 54, 354–373.
Azam, J.-P. (2002). Looting and conflict between ethnoregional groups: Lessons for state formation in Africa. Journal of Conflict Resolution, 46, 131–153.
Baliga, S., & Sjostrom, T. (2013). Bargaining and war: A review of some formal models. Korean Economic Review, 29, 235–266.
Barros, C., & Proena, I. (2005). Mixed logit estimation of radical Islamic terrorism in Europe and North America: A comparative study. Journal of Conflict Resolution, 49, 298–314.
Bevi, C., & Corchon, L. C. (2010). Peace agreements without commitment. Games and Economic Behavior, 68, 469–487.
Bevi, C., & Corchon, L. C. (2013). Endogenous strength in conflicts. International Journal of Industrial Organization, 31, 297–306.
Blimes, R. J. (2006). The indirect effect of ethnic heterogeneity on the likelihood of civil war onset. Journal of Conflict Resolution, 50, 536–547.
Blomberg, B. S., & Hess, G. D. (2002). The temporal links between conflict and economic activity. Journal of Conflict Resolution, 46, 74–90.
Blomberg, S. B., Hess, G. D., & Orphanides, A. (2004). The macroeconomic consequences of terrorism. Journal of Monetary Economics, 51, 1007–1032.
Boudreau, J. W., Rentschler, L. & Sanders, S. (2017). Stag hunt contests and alliance formation. Working Paper.
Brito, D., & Intriligator, M. (1985). Conflict, war and redistribution. American Political Science Review, 79, 943–957.
Brown, J. (2011). Quitters never win: The (adverse) incentive effects of competing with superstars. Journal of Political Economy, 119, 982–1013.
Carey, S., Colaresi, M. P., & Mitchell, N. J. (2015). Governments, informal links to militias, and accountability. Journal of Conflict Resolution, 59, 850–876.
Cederman, L.-E., & Gleditsch, K. S. (2009). Introduction to special issue on “Disaggregating Civil War”. Journal of Conflict Resolution, 53, 487–495.
Choudhury, S. M., & Sheremeta, R. M. (2011). Multiple equilibria in Tullock contests. Economics Letters, 112, 216–219.
Collier, P., & Duponchel, M. (2013). The economic legacy of civil war. Journal of Conflict Resolution, 57, 65–88.
Collier, P., & Hoeffler, A. (2002). On the incidence of civil war in Africa. Journal of Conflict Resolution, 46, 13–28.
Collier, P., & Sambanis, N. (2002). Understanding civil war. Journal of Conflict Resolution, 46, 3–12.
Corchon, L. C. (2007). The theory of contests: A survey. Review of Economic Design, 11, 69–100.
Corchon, L. C., & Serena, M. (2018). Contest theory: A survey. In L. C. Corchon & M. A. Marini (Eds.), Handbook of game theory and industrial organization (Vol. II, pp. 125–146). Northampton, MA: Edward Elgar Publishing.
Corchon, L. C., & Yildizparlak, A. (2013). Give peace a chance: The effect of ownership and asymmetric information on peace. Journal of Economic Behavior and Organization, 92, 116–126.
Dahm, M., & Porteiro, N. (2008). Biased contests. Public Choice, 136, 55–67.
de Mesquita, B. B., Morrow, J. D., Siverson, R., & Smith, A. (1999). An institutional explanation of the democratic peace. American Political Science Review, 93, 791–808.
Dixit, A. (1987). Strategic behavior in contests. American Economic Review, 77, 891–898.
Dodd, V. (2016). Isis planning ’enormous and spectacular attacks’, anti-terror chief warns. https://www.theguardian.com/uk-news/2016/mar/07/isis-planning-enormous-and-spectacular-attacks-uk-counter-terrorism-chief-warns. Accessed 20 Apr 2017.
Enders, W., & Sandler, T. (2000). Is transnational terrorism becoming more threatening? A time-series investigation. Journal of Conflict Resolution, 44, 307–332.
Enders, W., & Sandler, T. (2012). The political economy of terrorism. New York, NY: Cambridge University Press.
Faria, J. R., Silva, E., & Arce, A. (2017). Intertemporal versus spatial externalities in counterterror policy games. Dynamic Games and Applications, 7, 402–421.
Fearon, J. D., & Laitin, D. D. (2003). Ethnicity, insurgency, and civil war. American Political Science Review, 97, 75–90.
Fey, M., & Ramsay, K. (2007). Mutual optimism and war. American Journal of Political Science, 51, 738–754.
Filson, D., & Werner, S. (2002). A bargaining model of war and peace: Anticipating the onset, duration, and outcome of war. American Journal of Political Science, 46, 819–838.
Gaibulloev, K., & Sandler, T. (2009). The impact of terrorism and conflicts on growth in Asia. Economics and Politics, 21, 359–383.
Gause, F. G. (2014). ISIS and the new Middle East cold war. In Brookings Institution, Washington D.C.https://www.brookings.edu/blog/markaz/2014/08/25/isis-and-the-new-middle-east-cold-war/. Accessed 18 Jan 2017 .
Genicot, G., & Skaperdas, S. (2002). Investing in conflict management. Journal of Conflict Resolution, 46, 154–170.
Gleditsch, K. S., & Beardsley, K. (2004). Nosy neighbors: Third-party actors in Central American conflicts. Journal of Conflict Resolution, 48, 379–402.
Gleditsch, K. S., Salehyan, I., & Schultz, K. (2008). Fighting at home, fighting abroad: How civil wars lead to international disputes. Journal of Conflict Resolution, 52, 479–506.
Hinnebusch, R. (2014). Syria. In E. Lust (Ed.), The middle east (pp. 764–788). Washington: CQ Press.
Hirshleifer, J. (1989). Conflict and rent-seeking success functions: Ratio vs. difference models of relative success. Public Choice, 63, 101–112.
Hoffman, B. (2006). Inside terrorism. New York, NY: Columbia University Press.
Hwang, S. (2012). Technology of military conflict, military spending, and war. Journal of Public Economics, 96, 226–236.
Jackson, M., & Morelli, M. (2007). Political bias and war. American Economic Review, 97, 1353–1373.
Katz, E., Nitzan, S., & Rosenberg, J. (1990). Rent-seeking for pure public goods. Public Choice, 65, 49–60.
Klose, B., & Kovenock, D. (2015). The all-pay auction with complete information and identity-dependent externalities. Economic Theory, 59, 1–19.
Konrad, K. (2012). Dynamic contests and the discouragement effect. Revue d’Economie Politique, 122, 233–256.
Levy, A., & Faria, J. R. (2007). Ramsey in dual-population lands: Internal conflict and utility-maximizing consumption. Defence and Peace Economics, 18, 339–352.
Linster, B. G. (1993). A generalized model of rent-seeking behavior. Public Choice, 77, 421–435.
Moldovanu, B., & Sela, A. (2001). The optimal allocation of prizes in contests. American Economic Review, 91, 542–558.
Mollers, M. (2012). Incentives versus competitive balance. Economics Letters, 117, 505–508.
Murdoch, J. C., & Sandler, T. (2002a). Civil wars and economic growth: A regional comparison. Defence and Peace Economics, 13, 451–464.
Murdoch, J. C., & Sandler, T. (2002b). Economic growth, civil wars, and spatial spillovers. Journal of Conflict Resolution, 46, 91–110.
Oliveira, A. R., Faria, J. R., & Silva, E. (2018). Transnational terrorism: Externalities and coalition formation. Journal of Conflict Resolution, 62, 496–528.
Otto, S. (2017). The grass is always greener? Armed group side switching in civil wars. Journal of Conflict Resolution forthcoming. https://doi.org/10.1177/0022002717693047.
Phares, W. (2005). Future jihad. New York, NY: St. Martin’s Griffin.
Reynal-Querol, M. (2002). Ethnicity, political systems, and civil wars. Journal of Conflict Resolution, 46, 29–54.
Rogin, J. (2014). America’s allies are funding ISIS. In Daily Beast. http://www.thedailybeast.com/articles/2014/06/14/america-s-allies-are-funding-isis.html. Accessed 18 Jan 2017.
Russett, B., & Oneal, J. (2001). Triangulating peace: Democracy, interdependence, and international organizations. New York, NY: Norton.
Salehyan, I. (2010). The delegation of war to rebel organizations. Journal of Conflict Resolution, 54(3), 493–515.
Salehyan, I., Gleditsch, K. S., & Cunningham, D. E. (2011). Explaining external support for insurgent groups. International Organization, 65, 709–744.
Sambanis, N. (2001). Do ethnic and non-ethnic civil wars have the same causes? A theoretical and empirical inquiry (Part 1). Journal of Conflict Resolution, 45, 259–282.
Sanchez-Pages, S. (2007). Endogenous coalition formation in contests. Review of Economic Design, 11, 139–163.
Schelling, T. (1966). Arms and influence. New Haven, CT: Yale University Press.
Sela, A. (2011). Best-of-three all-pay auctions. Economics Letters, 112, 67–70.
Skaperdas, S. (1996). Contest success functions. Economic Theory, 7, 283–290.
Srli, M. E., Gleditsch, N. P., & Strand, H. (2005). Why is there so much conflict in the middle east? Journal of Conflict Resolution, 49, 141–165.
Staniland, P. (2012). Between a rock and a hard place: Insurgent fratricide, ethnic defection, and the rise of pro-state paramilitaries. Journal of Conflict Resolution, 56, 16–40.
Staniland, P. (2015). Militias, ideology and the state. Journal of Conflict Resolution, 59, 770–793.
Tavares, J. (2004). The open society assesses its enemies: Shocks, disasters and terrorist attacks. Journal of Monetary Economics, 51, 1039–1070.
Tir, J., & Jasinski, M. (2008). Domestic-level diversionary theory of war: Targeting ethnic minorities. Journal of Conflict Resolution, 52, 641–664.
Tullock, G. (1980). Efficient rent-seeking. In J. M. Buchanan, R. D. Tollison, & G. Tullock (Eds.), Toward a theory of the rent-seeking society (pp. 97–112). College Station, TX: Texas A&M University Press.
Wood, G. (2015). What ISIS really wants? In Atlantic. http://www.theatlantic.com/ magazine/archive/2015/03/what-isis-really-wants/384980/?utm_source=SFFBants. Accessed 20 Apr 2017.
Zollner, B. (2009). The muslim brotherhood: Hasan Al-Hudaybi and ideology. London: Palgrave.
Zorthian, J. (2015). Who’s fighting who in Syria. In Time. http://time.com/4059856/syria-civil-war-explainer/. Accessed 18 Jan 2017.
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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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DOI: https://doi.org/10.1007/s11127-018-0586-5