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Stationary Consistent Equilibrium Coalition Structures Constitute the Recursive Core

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  • Laszlo A. Koczy

    ()
    (Institute of Economics Research Centre for Economic and Regional Studies Hungarian Academy of Sciences)

Abstract

We study coalitional games where the coalitional payoffs depend on the entire coalition structure. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core, a generalisation of the core to such games. In order to extend past results limited to totally recursive-balanced partition function form games we introduce subgame-consistency that requires perfectness in relevant subgames only, while some unreached subgames are ignored. Due to the externalities, the profitability of deviations depends on the partition formed by the remaining players: the stability of core payoff configurations is ensured by a combination of the pessimism of players going for certain profits only and the assumption that players base their stationary strategies on a made-up history punishing some of the possible deviators - and getting this sometimes right.

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Bibliographic Info

Paper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 1226.

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Length: 26 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:has:discpr:1226

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Keywords: partition function; externalities; implementation; recursive core; stationary perfect equilibrium; time consistent equilibrium;

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References

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  1. Kyle Hyndman & Debraj Ray, 2007. "Coalition Formation with Binding Agreements," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1125-1147.
  2. Huang, Chen-Ying & Sjostrom, Tomas, 2006. "Implementation of the recursive core for partition function form games," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 771-793, September.
  3. Parkash Chander & Henry Tulkens, 1995. "A core-theoretic solution for the design of cooperative agreements on transfrontier pollution," International Tax and Public Finance, Springer, vol. 2(2), pages 279-293, August.
  4. Asilis, Carlos M., 1995. "A note on the equivalence of time consistency and subgame perfection in stochastic games," European Economic Review, Elsevier, vol. 39(2), pages 245-251, February.
  5. Sang-Seung, Yi, 1996. "Endogenous formation of customs unions under imperfect competition: open regionalism is good," Journal of International Economics, Elsevier, vol. 41(1-2), pages 153-177, August.
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  7. Ray, D. & Vohra, R., 1993. "Equilibrium Binding Agreements," Papers 21, Boston University - Department of Economics.
  8. Kóczy, László Á., 2009. "Sequential coalition formation and the core in the presence of externalities," Games and Economic Behavior, Elsevier, vol. 66(1), pages 559-565, May.
  9. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
  10. Huang, Chen-Ying & Sjostrom, Tomas, 2003. "Consistent solutions for cooperative games with externalities," Games and Economic Behavior, Elsevier, vol. 43(2), pages 196-213, May.
  11. Eyckmans, Johan & Tulkens, Henry, 2003. "Simulating coalitionally stable burden sharing agreements for the climate change problem," Resource and Energy Economics, Elsevier, vol. 25(4), pages 299-327, October.
  12. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-91, June.
  13. Francis Bloch, 1995. "Endogenous Structures of Association in Oligopolies," RAND Journal of Economics, The RAND Corporation, vol. 26(3), pages 537-556, Autumn.
  14. Chen-Ying Huang & Tomas Sjöström, 2010. "The Recursive Core for Non-Superadditive Games," Games, MDPI, Open Access Journal, vol. 1(2), pages 66-88, April.
  15. Fershtman, C., 1988. "Fixed Rules And Decision Rules: Time Consistency And Subgame Perfection," Papers 12-88, Tel Aviv.
  16. Muthoo, Abhinay, 1990. "Bargaining without commitment," Games and Economic Behavior, Elsevier, vol. 2(3), pages 291-297, September.
  17. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
  18. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer, vol. 28(2), pages 157-171.
  19. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 463-77, April.
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