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Coalitional Colonel Blotto games with application to the economics of alliances

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  • Kovenock, Dan
  • Roberson, Brian

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. -- Diese Arbeit analysiert Colonel Blotto-Spiele mit mehr als zwei Spielern, die an mindestens zwei Fronten miteinander kämpfen. Spieler A kämpft gleichzeitig in zwei Colonel Blotto-Spielen mit zwei verschiedenen Kontrahenten, B1 und B2. Die Kontrahenten können vor der eigentlichen Konfliktphase eine Allianz eingehen. Das erlaubt es ihnen ihre Mengen an einer homogenen Konfliktressource (Truppen, Waffen, Geld) untereinander zu transferieren. Das Papier untersucht dabei „nicht-kooperative“ Allianzen. Darunter wird verstanden, dass der Einsatz der transferierten Ressourcen auf den jeweiligen Konfliktschauplätzen von dem jeweiligen Spieler B1 bzw. B2 in seinem eigenen Interesse eingesetzt wird und Seitenzahlungen im Anschluss an die Konfliktphase ausgeschlossen sind. Es zeigt sich, dass es dennoch zu einseitigen und freiwilligen Ressourcentransfers der Spieler B1 und B2 im Vorfeld des Konflikts kommen kann, dass also beispielsweise B1 an B2 z.B. Waffen liefert, B2 diese als Geschenk akzeptiert und sich beide, B1 und B2 besser stellen. Ursache für die Besserstellung ist der strategische Effekt solcher Transfers auf das Kampfverhalten von A, der seine Kampfkraft vom Kampfgeschehen mit B1 zum Kampfgeschehen mit B2 verlagert. Das Ergebnis widerspricht den früheren Ergebnissen zu Allianzen (vgl. Sandler und Hartley, 2001), das im Kontext der privaten Bereitstellung öffentlicher Güter erzielt wurde.

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Bibliographic Info

Paper provided by Social Science Research Center Berlin (WZB) in its series Discussion Papers, Research Unit: Market Processes and Governance with number SP II 2008-02.

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Date of creation: 2008
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Handle: RePEc:zbw:wzbmpg:spii200802

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Related research

Keywords: Alliance; noncooperative game; Colonel Blotto game; self-enforcing; exploitation; commitment;

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References

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  1. Skaperdas, Stergios, 1998. " On the Formation of Alliances in Conflict and Contests," Public Choice, Springer, vol. 96(1-2), pages 25-42, July.
  2. 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.
  3. Sandler, Todd, 1977. "Impurity of Defense: An Application to the Economics of Alliances," Kyklos, Wiley Blackwell, vol. 30(3), pages 443-60.
  4. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  5. 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.
  6. 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.
  7. Sandler, Todd, 1999. "Alliance Formation, Alliance Expansion, and the Core," Staff General Research Papers 1669, Iowa State University, Department of Economics.
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Citations

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Cited by:
  1. Changxia Ke & Kai A. Konrad & Florian Morath, 2011. "Brothers in Arms - An Experiment on the Alliance Puzzle," Working Papers brothers_in_arms, Max Planck Institute for Tax Law and Public Finance.
  2. Kai A. Konrad & Dan Kovenock, 2008. "The Alliance Formation Puzzle and Capacity Constraints," Purdue University Economics Working Papers 1209, Purdue University, Department of Economics.
  3. Kai A. Konrad, 2011. "Strategie Aspects of Fighting in Alliances," Working Papers strategie_aspects_of_figh, Max Planck Institute for Tax Law and Public Finance.
  4. 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).
  5. Kai Konrad, 2012. "Information alliances in contests with budget limits," Public Choice, Springer, vol. 151(3), pages 679-693, June.
  6. Brian Roberson & Dmitriy Kvasov, 2012. "The non-constant-sum Colonel Blotto game," Economic Theory, Springer, vol. 51(2), pages 397-433, October.
  7. 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.
  8. K.J.M. De Jaegher & B. Hoyer, 2012. "Cooperation and the common enemy effect," Working Papers 12-24, Utrecht School of Economics.
  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. 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.

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