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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. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
  2. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  3. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
  4. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  5. 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).
  6. 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.
  7. 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).
  8. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  9. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  11. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  12. Krishna, Vijay & Serrano, Roberto, 1995. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," International Journal of Game Theory, Springer, vol. 24(3), pages 259-72.
  13. 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.
  14. Volij, Oscar & Serrano, Roberto, 1998. "Axiomatizations of Neoclassical Concepts for Economies," Staff General Research Papers 5192, Iowa State University, Department of Economics.
  15. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
  16. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  17. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  18. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
  19. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
  20. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  21. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
  22. Perry, M. & Rany, P., 1992. "A Non-Cooperative View of Coalition Formation and the Core," UWO Department of Economics Working Papers 9203, University of Western Ontario, Department of Economics.
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Cited by:
  1. Roberto Serrano, 2009. "On Watson'S Non-Forcing Contracts And Renegotiation," Working Papers wp2009_0907, CEMFI.
  2. Repullo, Rafael & Suarez, Javier, 2008. "The Procyclical Effects of Basel II," CEPR Discussion Papers 6862, C.E.P.R. Discussion Papers.
  3. Roberto Serrano & Yusuke Kamishiro, 2009. "Equilibrium Blocking In Large Quasilinear Economies," Working Papers wp2009_0911, CEMFI.
  4. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," CeMMAP working papers CWP24/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Working Papers 2009-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  6. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  7. Joan Llull, 2008. "The Impact Of Immigration On Productivity," Working Papers wp2008_0802, CEMFI.
  8. Rafael Repullo & David Martínez-Miera, 2008. "Does Competition Reduce The Risk Of Bank Failure?," Working Papers wp2008_0801, CEMFI.

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