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Coalition Formation in Political Games

  • Daron Acemoglu
  • Georgy Egorov
  • Konstantin Sonin

We study the formation of a ruling coalition in political environments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternative coalition that may challenge it, and it needs to be self-enforcing, in the sense that none of its sub-coalitions should be able to secede and become the new ruling coalition. We first present an axiomatic approach that captures these notions and determines a (generically) unique ruling coalition. We then construct a simple dynamic game that encompasses these ideas and prove that the sequentially weakly dominant equilibria (and the Markovian trembling hand perfect equilibria) of this game coincide with the set of ruling coalitions of the axiomatic approach. We also show the equivalence of these notions to the core of a related non-transferable utility cooperative game. In all cases, the nature of the ruling coalition is determined by the power constraint, which requires that the ruling coalition be powerful enough, and by the enforcement constraint, which imposes that no sub-coalition of the ruling coalition that commands a majority is self-enforcing. The key insight that emerges from this characterization is that the coalition is made self-enforcing precisely by the failure of its winning sub-coalitions to be self-enforcing. This is most simply illustrated by the following simple finding: with a simple majority rule, while three-person (or larger) coalitions can be self-enforcing, two-person coalitions are generically not self-enforcing. Therefore, the reasoning in this paper suggests that three-person juntas or councils should be more common than two-person ones. In addition, we provide conditions under which the grand coalition will be the ruling coalition and conditions under which the most powerful individuals will not be included in the ruling coalition. We also use this framework to discuss endogenous party formation.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12749.

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Date of creation: Dec 2006
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Publication status: published as Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2008. "Coalition Formation in Non-Democracies," Review of Economic Studies, Wiley Blackwell, vol. 75(4), pages 987-1009, October.
Handle: RePEc:nbr:nberwo:12749
Note: POL
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  1. Moldovanu, Benny, 1992. "Coalition-proof nash equilibria and the core in three-player games," Games and Economic Behavior, Elsevier, vol. 4(4), pages 565-581, October.
  2. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  3. Greenberg, J. & Weber, S., 1991. "Stable Coalition Structure with Unidimensional Set of Alternatives," Papers 91-11, York (Canada) - Department of Economics.
  4. Peleg, Bezalel & Rosenmuller, Joachim, 1992. "The least core, nucleolus, and kernel of homogeneous weighted majority games," Games and Economic Behavior, Elsevier, vol. 4(4), pages 588-605, October.
  5. Hideo Konishi & Debraj Ray, 2000. "Coalition Formation as a Dynamic Process," Boston College Working Papers in Economics 478, Boston College Department of Economics, revised 15 Apr 2002.
  6. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  7. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
  8. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August.
  9. Greenberg Joseph & Weber Shlomo, 1993. "Stable Coalition Structures with a Unidimensional Set of Alternatives," Journal of Economic Theory, Elsevier, vol. 60(1), pages 62-82, June.
  10. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  11. Peleg, Bezalel, 1980. "A theory of coalition formation in committees," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 115-134, July.
  12. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1355-1384, December.
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