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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. 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.
  2. 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.
  3. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  4. Krishna, V. & serrano, R., 1993. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," Papers 10-93-31, Pennsylvania State - Department of Economics.
  5. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  6. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  7. 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.
  8. 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).
  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. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
  11. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  12. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  13. Perez-Castrillo J. David, 1994. "Cooperative Outcomes through Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 428-440, November.
  14. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
  15. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  16. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
  17. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  18. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
  19. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
  20. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  21. Volij, Oscar & Serrano, Roberto, 1998. "Axiomatizations of Neoclassical Concepts for Economies," Staff General Research Papers 5192, Iowa State University, Department of Economics.
  22. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
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Citations

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Cited by:
  1. 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.
  2. Joan Llull, 2008. "The Impact Of Immigration On Productivity," Working Papers wp2008_0802, CEMFI.
  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?," Working Papers wp2009_0905, CEMFI.
  5. Repullo, Rafael & Suarez, Javier, 2008. "The Procyclical Effects of Basel II," CEPR Discussion Papers 6862, C.E.P.R. Discussion Papers.
  6. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  7. Roberto Serrano, 2009. "On Watson'S Non-Forcing Contracts And Renegotiation," Working Papers wp2009_0907, 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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