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Coalitional Colonel Blotto Games with Application to the Economics of Alliances

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  • Dan Kovenock
  • Brian Roberson

Abstract

This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g., troops, military hardware, money). This paper examines “non-cooperative” alliances in which only individually rational ex ante transfers of the resource are allowed. Once these transfers take place, each alliance member maximizes his payoff in his respective Colonel Blotto game, given his resource constraint and player A’s allocation of its endowment across the two games. No ex post transfers are enforceable. Remarkably, there are several ranges of parameters in which endogenous unilateral transfers take place within the alliance. That is, one player gives away resources to his ally, who happily accepts the gift. Unilateral transfers arise because they lead to a strategic shift in the common opponent’s force allocation away from the set of battlefields of the player making the transfer, towards the set of battlefields of the player receiving the transfer. Our result demonstrates that there exist unilateral transfers for which the combination of direct and strategic effects benefits both allies. This stands in stark contrast to the previous literature on alliances (see Sandler and Hartley, 2001), which relies on the assumption of pure or impure public goods.

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Bibliographic Info

Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1207.

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Length: 25 pages
Date of creation: Nov 2007
Date of revision:
Handle: RePEc:pur:prukra:1207

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  1. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  2. Keith Hartley & Todd Sandler, 2001. "Economics of Alliances: The Lessons for Collective Action," Journal of Economic Literature, American Economic Association, vol. 39(3), pages 869-896, September.
  3. Skaperdas, Stergios, 1998. " On the Formation of Alliances in Conflict and Contests," Public Choice, Springer, vol. 96(1-2), pages 25-42, July.
  4. Sandler, Todd, 1977. "Impurity of Defense: An Application to the Economics of Alliances," Kyklos, Wiley Blackwell, vol. 30(3), pages 443-60.
  5. Sandler, Todd, 1999. "Alliance Formation, Alliance Expansion, and the Core," Staff General Research Papers 1669, Iowa State University, Department of Economics.
  6. Arce M, Daniel G & Sandler, Todd, 2001. " A Cooperative Game Theory of Noncontiguous Allies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(4), pages 391-411.
  7. Murdoch, James C. & Sandler, Todd, 1984. "Complementarity, free riding, and the military expenditures of NATO allies," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 83-101, November.
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Cited by:
  1. Konrad, Kai A. & Kovenock, Dan, 2009. "The alliance formation puzzle and capacity constraints," Economics Letters, Elsevier, vol. 103(2), pages 84-86, May.
  2. Konrad, Kai A. & Ke, Changxia & Morath, Florian, 2012. "Brothers in Arms - An Experiment on the Alliance Puzzle," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62038, Verein für Socialpolitik / German Economic Association.
  3. Konrad, Kai A., 2011. "Strategic aspects of fighting in alliances," Discussion Papers, Research Professorship & Project "The Future of Fiscal Federalism" SP II 2011-105, Social Science Research Center Berlin (WZB).
  4. Konrad, Kai A., 2010. "Information alliances in contests with budget limits," Discussion Papers, Research Professorship & Project "The Future of Fiscal Federalism" SP II 2010-21, Social Science Research Center Berlin (WZB).
  5. John Duffy & Alexander Matros, 2013. "Stochastic Asymmetric Blotto Games: Theory and Experimental Evidence," Working Papers 509, University of Pittsburgh, Department of Economics, revised Nov 2013.
  6. Konrad, Kai A., 2010. "Dynamic contests," Discussion Papers, Research Professorship & Project "The Future of Fiscal Federalism" SP II 2010-10, Social Science Research Center Berlin (WZB).
  7. K.J.M. De Jaegher & B. Hoyer, 2012. "Cooperation and the common enemy effect," Working Papers 12-24, Utrecht School of Economics.
  8. Brian Roberson & Dmitriy Kvasov, 2012. "The non-constant-sum Colonel Blotto game," Economic Theory, Springer, vol. 51(2), pages 397-433, October.
  9. Herbst, Luisa & Konrad, Kai A. & Morath, Florian, 2013. "Endogenous group formation in experimental contests," Discussion Papers, Research Unit: Economics of Change SP II 2013-301, Social Science Research Center Berlin (WZB).
  10. Herbst, Luisa & Konrad, Kai A. & Morath, Florian, 2013. "Endogenous group formation in experimental contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 419, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.

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