Abstract
We investigate the implications of balanced consistency and balanced cost reduction in the context of sequencing problems. Balanced consistency requires that the effect on the payoff from the departure of one agent to another agent should be equal between any two agents. On the other hand, balanced cost reduction requires that if one agent leaves a problem, then the total payoffs of the remaining agents should be affected by the amount previously assigned to the leaving agent. We show that the minimal transfer rule is the only rule satisfying efficiency and Pareto indifference together with either one of our two main axioms, balanced consistency and balanced cost reduction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Chun Y (1986) The solidarity axiom for quasi-linear social choice problems. Soc Choice Welf 3: 297–310
Chun Y (2011) Consistency and monotonicity in sequencing problems. Int J Game Theory 40: 29–41
Chun Y (2006) A pessimistic approach to the queueing problem. Math Soc Sci 51: 171–181
Chun Y (2006) No-envy in queueing problems. Econ Theory 29: 151–162
Curiel I, Pederzoli G, Tijs S (1989) Sequencing games. Eur J Oper Res 40: 344–351
Dolan R (1978) Incentive mechanisms for priority queueing problems. Bell J Econ 9: 421–436
Harsanyi JC (1959) A bargaining model for cooperative n-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV. Princeton UP, Princeton, pp 325–355
Hart S, Mas-Colell A (1989) Potential, value and consistency. Econometrica 57: 589–614
Maniquet F (2003) A characterization of the Shapley value in queueing problems. J Econ Theory 109: 90–103
Mishra D, Rangarajan B (2007) Cost sharing in a job scheduling problem. Soc Choice Welf 29: 369–382
Mitra M (2001) Mechanism design in queueing problems. Econ Theory 17: 277–305
Mitra M (2002) Achieving the first best in sequencing problems. Rev Econ Des 7: 75–91
Moulin H (2007) On scheduling fees to prevent merging, splitting, and transferring of jobs. Math Oper Res 32: 266–283
Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2: 225–229
Myerson RB (1980) Conference structures and fair allocation rules. Int J Game Theory 9: 169–182
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II, Annals of mathematics studies No 28. Princeton University Press, Princeton, NJ, pp 307–317
Smith W (1956) Various optimizers for single-stage production. Nav Res Logist Q 3: 59–66
Suijs J (1996) On incentive compatibility and budget balancedness in public decision making. Econ Des 2: 193–209
Thomson W (1983) Problems of fair division and the egalitarian solution. J Econ Theory 31: 211–226
Thomson W (1995) Population monotonic allocation rules. In: Barnett WA, Moulin H, Salles M, Schofield NJ (eds) Social choice, welfare, and ethics. Cambridge University Press, Cambridge, pp 79–124
van den Brink R (2001) An axiomatization of the Shapley value using a fairness property. Int J Game Theory 30: 309–319
van den Brink R (2007) Null or nullifying players: the difference between the Shapley value and equal division solutions. J Econ Theory 136: 767–775
van den Brink R, van der Laan G, Vasil’ev VA (2007) Component efficient solutions in line-graph games with applications. Econ Theory 33: 349–364
Young HP (1985) Monotonic solutions of cooperative games. Int J Game Theory 14: 65–72
Acknowledgments
The authors are grateful to Kyung Hwan Baik, Francois Maniquet, and two referees for their comments. Chun’s work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (KRF-2009-342-B00011) and the Netherlands Organization for Scientific Research (NWO) grant 040.11.143.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
van den Brink, R., Chun, Y. Balanced consistency and balanced cost reduction for sequencing problems. Soc Choice Welf 38, 519–529 (2012). https://doi.org/10.1007/s00355-011-0533-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-011-0533-6