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A non-cooperative approach to the ordinal Shapley rule

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  • Vidal-Puga, Juan

Abstract

In bargaining problems, a rule satisfies ordinal invariance if it does not depend on order-preserving transformations of the agents' utilities. In this paper, a simple non-cooperative game for three agents, based on bilateral offers, is presented. The ordinal Shapley rule arises in subgame perfect equilibrium as the agents have more time to reach an agreement.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43790.

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Date of creation: 14 Jan 2013
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Handle: RePEc:pra:mprapa:43790

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Keywords: ordinal bargaining; ordinal Shapley rule;

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  1. Kibris, Ozgur, 2004. "Ordinal invariance in multicoalitional bargaining," Games and Economic Behavior, Elsevier, Elsevier, vol. 46(1), pages 76-87, January.
  2. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, Fundación SEPI, vol. 29(2), pages 219-258, May.
  3. Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, Elsevier, vol. 19(2), pages 151-179, May.
  4. Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, Elsevier, vol. 52(1), pages 20-33, July.
  5. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, Econometric Society, vol. 64(2), pages 357-80, March.
  6. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 274-294, October.
  7. David Pérez-Castrillo & David Wettstein, 2005. "Implementation of the Ordinal Shapley Value for a three-agent economy," Economics Bulletin, AccessEcon, vol. 3(48), pages 1-8.
  8. Suresh Mutuswami & Eyal Winter, 2001. "Subscription Mechanisms for Network Formation," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp264, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
  10. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, Econometric Society, vol. 56(5), pages 1191-1220, September.
  11. Perez-Castrillo, David & Wettstein, David, 2006. "An ordinal Shapley value for economic environments," Journal of Economic Theory, Elsevier, Elsevier, vol. 127(1), pages 296-308, March.
  12. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
  13. Bag, Parimal Kanti & Winter, Eyal, 1999. "Simple Subscription Mechanisms for Excludable Public Goods," Journal of Economic Theory, Elsevier, Elsevier, vol. 87(1), pages 72-94, July.
  14. Kibris, Ozgur, 2004. "Egalitarianism in ordinal bargaining: the Shapley-Shubik rule," Games and Economic Behavior, Elsevier, Elsevier, vol. 49(1), pages 157-170, October.
  15. Özgür Kıbrıs, 2012. "Nash bargaining in ordinal environments," Review of Economic Design, Springer, Springer, vol. 16(4), pages 269-282, December.
  16. David P�rez-Castrillo & David Wettstein, 2002. "Choosing Wisely: A Multibidding Approach," American Economic Review, American Economic Association, American Economic Association, vol. 92(5), pages 1577-1587, December.
  17. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  18. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, Econometric Society, vol. 45(7), pages 1623-30, October.
  19. repec:ebl:ecbull:v:3:y:2005:i:48:p:1-8 is not listed on IDEAS
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