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Cooperative Games: Core and Shapley Value

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This article describes the basic elements of the cooperative approach to game theory, one of the two counterparts of the discipline. After the presentation of some basic definitions, the focus will be on the core and the Shapley value, two of the most central solution concepts in cooperative game theory.

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File URL: http://www.brown.edu/Departments/Economics/Papers/2007/2007-11_paper.pdf
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Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2007-11.

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Date of creation: 2007
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Handle: RePEc:bro:econwp:2007-11

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Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Geoffroy de Clippel & Hans Peters & Horst Zank, 2004. "Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games," International Journal of Game Theory, Springer, vol. 33(1), pages 145-158, January.
  2. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  3. Peraz-Castrillo, J., 1992. "Cooperative Outcomes Through Non-Cooperative Games," UFAE and IAE Working Papers 165.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. AUMANN, Robert J., . "Values of markets with a continuum of traders," CORE Discussion Papers RP -228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Serrano, Roberto & Volij, Oscar, 1998. "Axiomatizations of neoclassical concepts for economies," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 87-108, August.
  6. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
  7. Krishna, V. & serrano, R., 1993. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," Papers 10-93-31, Pennsylvania State - Department of Economics.
  8. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
  9. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
  10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  11. David Pérez-Castrillo & David Wettstein, . "Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value," UFAE and IAE Working Papers 461.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  12. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
  13. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  14. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  15. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  16. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  17. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  18. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
  19. 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.
  20. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  21. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
  22. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium blocking in large quasilinear economies," Working Papers 2009-12, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  2. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," Working Papers wp2009_0905, CEMFI.
  3. Roberto Serrano, 2004. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Working Papers 0041, Institute for Advanced Study, School of Social Science.
  4. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity Of Mixed Equilibria In Mechanisms: A Unified Approach To Exact And Approximate Implementation," Working Papers wp2009_0908, CEMFI.
  5. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  6. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," Review of Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
  7. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers wp2008_0809, CEMFI.
  8. Joan Llull, 2008. "The Impact Of Immigration On Productivity," Working Papers wp2008_0802, CEMFI.

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