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Bargaining with intertemporal maximin payoffs

  • Vincent Martinet
  • Pedro Gajardo
  • Michel De Lara
  • Héctor Ramírez Cabrera

We present a new class of dynamic bargaining problems, called "bargaining problems with intertemporal maximin payoffs," that may reflect sustainability problems having to encompass conflicting issues in the long-run. Each bargainer (or stake-holder) has a representative indicator, namely a function of the state and decisions, and aims at maximizing its minimal value over time. Bargaining on sustainability issues consists in defining the vector of stake-holder's payoffs. We are interested in defining the set of feasible outcomes of such problems. This set is interpreted as a support for a social choice of sustainability objectives. We introduce a MONDAI condition – Monotonicity of Dynamics And Indicators – consistent with many economic problems and, in particular, "environmental economic" sustainability issues. We characterize the set of feasible outcomes for problems satisfying these monotonicity properties, and the bargaining solutions under the axioms of Pareto efficiency and Independence of Irrelevant Alternatives. We also provide a "satisficing" common decision rule to achieve any given solution. We then examine the time-consistency of the solution under the axioms of Veto Power and Individual Rationality.

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Paper provided by University of Paris West - Nanterre la Défense, EconomiX in its series EconomiX Working Papers with number 2011-7.

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Length: 37 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:drm:wpaper:2011-7
Contact details of provider: Postal: 200 Avenue de la République, Bât. G - 92001 Nanterre Cedex
Web page: http://economix.fr
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  1. Kalai, Ehud & Samet, Dov, 1985. "Monotonic Solutions to General Cooperative Games," Econometrica, Econometric Society, vol. 53(2), pages 307-27, March.
  2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  3. Martinet, Vincent, 2011. "A characterization of sustainability with indicators," Journal of Environmental Economics and Management, Elsevier, vol. 61(2), pages 183-197, March.
  4. Border, K.C. & Segal, U., 1995. "Preferences Over Solutions to the Margaining Probem," UWO Department of Economics Working Papers 9518, University of Western Ontario, Department of Economics.
  5. Cairns, Robert D. & Long, Ngo Van, 2006. "Maximin: a direct approach to sustainability," Environment and Development Economics, Cambridge University Press, vol. 11(03), pages 275-300, June.
  6. Kalai, Ehud & Pazner, Elisha A & Schmeidler, David, 1976. "Collective Choice Correspondences as Admissible Outcomes of Social Bargaining Processes," Econometrica, Econometric Society, vol. 44(2), pages 233-40, March.
  7. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  8. Mody, Ashoka & Roy, Subhendu & Wheeler, David & Dasgupta, Susmita, 1995. "Environmental regulation and development : a cross-country empirical analysis," Policy Research Working Paper Series 1448, The World Bank.
  9. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer, vol. 13(2), pages 231-257, April.
  10. Border, Kim C. & Segal, Uzi, 1995. "Preferences Over Solution to the Bargaining Problem," Working Papers 923, California Institute of Technology, Division of the Humanities and Social Sciences.
  11. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, vol. 45(1), pages 1-31, June.
  12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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