A new two-party bargaining mechanism
- 198 Downloads
- 4 Citations
Abstract
If resources and facilities from different partners need to be engaged for a large-scale project with a huge number of tasks, any of which is indivisible, decision on the number of tasks assigned to any collaborating partner often requires a certain amount of coordination and bargaining among these partners so that the ultimate task allocation can be accepted by any partner in a business union for the project. In the current global financial crisis, such cases may appear frequently. In this paper, we first investigate the behavior of such a discrete bargaining model often faced by service-based organizations. In particular, we address the general situation of two partners, where the finite Pareto efficient (profit allocation) set does not possess any convenient assumption for deriving a bargaining solution, namely a final profit allocation (corresponding to a task assignment) acceptable to both partners. We show that it is not appropriate for our discrete bargaining model to offer the union only one profit allocation. Modifying the original optimization problem used to derive the Nash Bargaining Solution (NBS), we develop a bargaining mechanism and define a related bargaining solution set to fulfil one type of needs on balance between profit-earning efficiency and profit-earning fairness. We then show that our mechanism can also suit both Nash’s original concave bargaining model and its continuous extension without the concavity of Pareto efficient frontier on profit allocation.
Keywords
Project Bargaining model Bargaining mechanism Bargaining solution set BalancePreview
Unable to display preview. Download preview PDF.
References
- Anant TCA, Mukherji B, Basu K (1990) Bargaining without convexity: generalizing the Kalai–Smorodinsky solution. Economics 33(2):115–119 MathSciNetGoogle Scholar
- Cao XR (1982) Preference functions and bargaining solutions. In: Proc IEEE conf decision and control, pp 164–171 Google Scholar
- Cao XR, Shen H, Milito R, Wirth P (2002) Internet pricing with a game theoretical approach: concepts and examples. IEEE/ACM Trans Netw 10:208–216 CrossRefGoogle Scholar
- Chen QL, Cai XQ (2004) Application on NBS for a negotiable third-party scheduling problem with a due window. In: ICSSSM 2004, pp 116–119 Google Scholar
- Chen QL (2006) A new discrete bargaining model on job partition between two manufacturers. PhD diss, Faculty of Engineering, The Chinese University of Hong Kong, Hong Kong Google Scholar
- Chen QL, Cai XQ, Gu YH (2006) An optimization problem on two-partition of jobs for profit allocation. In: APCCAS 2006, pp 626–629 Google Scholar
- Conley J, Wilkie S (1991) The bargaining problem without convexity: extending the egalitarian and Kalai–Smorodinsky solutions. Econ Lett 36:365–369 MathSciNetMATHCrossRefGoogle Scholar
- Dagan N, Volij O, Winter E (2002) A characterization of the Nash bargaining solution. Soc Choice Welf 19:811–823 MathSciNetMATHCrossRefGoogle Scholar
- Dong L, Liu H (2007) Equilibrium forward contracts on nonstorable commodities in the presence of market power. Oper Res 55:128–145 MathSciNetMATHCrossRefGoogle Scholar
- Gan XB, Gu YH, Vairaktarakis GL, Cai XQ, Chen QL (2007) A scheduling problem with one producer and the bargaining counterpart with two producers. In: ESCAPE 2007, pp 305–316 Google Scholar
- Gurnani N, Shi MZ (2006) A bargaining model for a first-time interaction under asymmetric beliefs of supply reliability. Manag Sci 52:865–880 MATHCrossRefGoogle Scholar
- Herrero MJ (1989) The Nash program: nonconvex bargaining problems. J Econ Theory 49:266–277 MathSciNetMATHCrossRefGoogle Scholar
- Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problems. Econometrica 43:513–518 MathSciNetMATHCrossRefGoogle Scholar
- Lahiri S (2004) Axiomatic characterization of the Nash and Kalai–Smorodinsky solutions for discrete bargaining problems. Pure Math Appl 14:207–220 MATHGoogle Scholar
- Mariotti M (1998) Nash bargaining theory when the number of alternatives can be finite. Soc Choice Welf 15:413–421 MathSciNetMATHCrossRefGoogle Scholar
- Muthoo A (1999) Bargaining theory with applications. Cambridge University Press, Cambridge MATHGoogle Scholar
- Nagahisa R, Tanaka M (2002) An axiomatization of the Kalai–Smorodinsky solution when the feasible sets can be finite. Soc Choice Welf 19:751–761 MathSciNetMATHCrossRefGoogle Scholar
- Nash JF (1950) The bargaining problem. Econometrica 18:155–162 MathSciNetMATHCrossRefGoogle Scholar
- Nash JF (1953) Two person cooperative games. Econometrica 21:128–140 MathSciNetMATHCrossRefGoogle Scholar
- Raiffa H (1953) Arbitration schemes for generalized two-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of game II. Princeton University Press, Princeton, pp 361–387 Google Scholar
- Saaty TL (1980) The analytic hierarchy process: planning, priority setting, resource allocation. McGraw-Hill, New York MATHGoogle Scholar
- Thomson W (1981) Nash’s bargaining solution and utilitarian choice rules. Econometrica 49:535–538 MathSciNetMATHCrossRefGoogle Scholar
- Touati C, Altman E, Galtier J (2006) Generalized Nash bargaining solution for bandwidth allocation. Comput Netw 50:3242–3263 MATHCrossRefGoogle Scholar
- Trockel W (2002) Integrating the Nash program into mechanism theory. Rev Econ Des 7:27–43 MathSciNetMATHGoogle Scholar
- Trockel W (2005) Core-equivalence for the Nash bargaining solution. Econ Theory 25:255–263 MathSciNetMATHCrossRefGoogle Scholar
- Zhang D (2005) A logical model of Nash bargaining solution. In: IJCAI, pp 983–990 Google Scholar