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Modelling Negotiated Decision Making: a Multilateral, Multiple Issues, Non-Cooperative Bargaining Model with Uncertainty

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Author Info
Alessandra Sgobbi (Fondazione Eni Enrico Mattei)
Carlo Carraro (University of Venice, Fondazione Eni Enrico Mattei and EuroMediterranean Center on Climate Change)

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Abstract

The relevance of bargaining to everyday life can easily be ascertained, yet the study of any bargaining process is extremely hard, involving a multiplicity of questions and complex issues. The objective of this paper is to provide new insights on some dimensions of the bargaining process – asymmetries and uncertainties in particular – by using a non-cooperative game theory approach. We develop a computational model which simulates the process of negotiation among more than two players, who bargain over the sharing of more than one pie. Through numerically simulating several multiple issues negotiation games among multiple players, we identify the main features of players’ optimal strategies and equilibrium agreements. As in most economic situations, uncertainty crucially affects also bargaining processes. Therefore, in our analysis, we introduce uncertainty over the size of the pies to be shared and assess the impacts on players’ strategic behaviour. Our results confirm that uncertainty crucially affects players’ behaviour and modifies the likelihood of a self-enforcing agreement to emerge. The model proposed here can have several applications, in particular in the field of natural resource management, where conflicts over how to share a resource of a finite size are increasing.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2007.81.

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Date of creation: Jul 2007
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Handle: RePEc:fem:femwpa:2007.81

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Related research
Keywords: Bargaining; Non-Cooperative Game Theory; Simulation Models; Uncertainty;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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  1. Ma, Ching-To Albert & Manove, Michael, 1993. "Bargaining with Deadlines and Imperfect Player Control," Econometrica, Econometric Society, vol. 61(6), pages 1313-39, November. [Downloadable!] (restricted)
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  2. Manzini, Paola & Mariotti, Marco, 2003. "A bargaining model of voluntary environmental agreements," Journal of Public Economics, Elsevier, vol. 87(12), pages 2725-2736, December. [Downloadable!] (restricted)
  3. Inderst, Roman, 2000. "Multi-issue Bargaining with Endogenous Agenda," Games and Economic Behavior, Elsevier, vol. 30(1), pages 64-82, January. [Downloadable!] (restricted)
  4. Carraro, Carlo & Siniscalco, Domenico, 1995. "R&D Cooperation and the Stability of International Environmental Agreements," CEPR Discussion Papers 1154, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  5. Younghwan In & Roberto Serrano, 2000. "Agenda Restrictions in Multi-Issue Bargaining," Working Papers 2000-08, Brown University, Department of Economics.
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  6. Henk Folmer & Pierre Mouche & Shannon Ragland, 1993. "Interconnected games and international environmental problems," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 3(4), pages 313-335, August. [Downloadable!] (restricted)
  7. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January. [Downloadable!] (restricted)
  8. Antonio Merlo & Daniel Diermeier & Hülya Eraslan, 2004. "Bicameralism and Government Formation," Working Papers 2004.81, Fondazione Eni Enrico Mattei. [Downloadable!]
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  10. Chae, Suchan & Yang, Jeong-Ae, 1988. "The unique perfect equilibrium of an n-person bargaining game," Economics Letters, Elsevier, vol. 28(3), pages 221-223. [Downloadable!] (restricted)
  11. Manzini, Paola & Mariotti, Marco, 2005. "Alliances and negotiations," Journal of Economic Theory, Elsevier, vol. 121(1), pages 128-141, March. [Downloadable!] (restricted)
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  12. Adams, Gregory & Rausser, Gordon & Simon, Leo, 1996. "Modelling multilateral negotiations: An application to California water policy," Journal of Economic Behavior & Organization, Elsevier, vol. 30(1), pages 97-111, July. [Downloadable!] (restricted)
  13. Bac, Mehmet & Raff, Horst, 1996. "Issue-by-Issue Negotiations: The Role of Information and Time Preference," Games and Economic Behavior, Elsevier, vol. 13(1), pages 125-134, March. [Downloadable!] (restricted)
  14. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March. [Downloadable!] (restricted)
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  15. Carraro, Carlo & Marchiori, Carmen & Sgobbi, Alessandra, 2007. "Negotiating on water: insights from non-cooperative bargaining theory," Environment and Development Economics, Cambridge University Press, vol. 12(02), pages 329-349, April. [Downloadable!]
  16. Gneezy, Uri & Haruvy, Ernan & Roth, Alvin E., 2003. "Bargaining under a deadline: evidence from the reverse ultimatum game," Games and Economic Behavior, Elsevier, vol. 45(2), pages 347-368, November. [Downloadable!] (restricted)
  17. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Blackwell Publishing, vol. 63(1), pages 61-80, January. [Downloadable!] (restricted)
  18. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March. [Downloadable!] (restricted)
  19. Fershtman, Chaim, 1990. "The importance of the agenda in bargaining," Games and Economic Behavior, Elsevier, vol. 2(3), pages 224-238, September. [Downloadable!] (restricted)
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  20. Sophie Thoyer & Sylvie Morardet & Patrick Rio & Leo Simon & Rachel Goodhue & Gordon Rausser, 2001. "A Bargaining Model to Simulate Negotiations Between Water Users," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 4. [Downloadable!]
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