What if Achilles and the tortoise were to bargain? An argument against interim agreements

Samet, Dov (2009): What if Achilles and the tortoise were to bargain? An argument against interim agreements.

Abstract

Zeno's paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement is concerned. Parkinson's Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements and using arguments similar to Zeno's, we show that if utilities are von Neumann-Morgenstern, then no such process can bring about an agreement in finite time in linear bargaining problems. To extend this result for all bargaining problems, we characterize a particular path illustrated by \cite{ra}, and show that no agreement is reached along this path in finite time.

• Item Type: MPRA Paper
• Language: English
• Keywords: Zeno's paradox, bargaining problems, interim agreements, vNM utility
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D73 - Bureaucracy ; Administrative Processes in Public Organizations ; Corruption; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D74 - Conflict ; Conflict Resolution ; Alliances ; Revolutions; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior

References

Anbarci, N., and C. Sun, (2009). Robustness of Intermediate Agreements and Bargaining Solutions, Economics Series 2009-14, Deakin University, Faculty of Business and Law.

Diskin A., M. Koppel, and D. Samet, (2010). Generalized Raiffa Solutions, a manuscript.

Kalai, E., (1977). Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparison, Econometrica, 45, 1623-1630.

Livne, Z. A., (1989). On the Status Quo Sets Induced by the Raiffa Solution to the Two-Person Bargaining Problem, Mathematics of Operations Research, 14, 688-692.

Luce, R. D., and H. Raiffa, (1957). Games and Decisions, Wiley, New York.

Nash, J., (1950). The Bargaining Problem, Econometrica, 18, 155-162.

O’Neill, B., D. Samet, Z. Wiener, and E. Winter, (2004). Bargaining with an Agenda, Games and Economic Behavior, 48, 139-153.

Parkinson, C.N., (1957). Parkinson’s Law and Other Studies in Administration, Houghton Mifflin Comapany, Boston.

Peters, H., and E. van Damme, (1993). Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement-point Axioms, Mathematics of Operations Research, 16, 447-461.

Quandt, W., (2005). Peace Process: American Diplomacy and the Arab-Israeli Conflict since 1967, Brookings Institution and University of California Press, Washington, DC.

Raiffa, H., (1953). Arbitration Schemes for Generalized Two-Person Games, In Contributions to the Theory of Games II, H.W. Kuhn and A.W. Tucker eds., Princeton University Press, Princeton New Jersey.

Thomson, W., (1987). Monotonicity of Bargaining Solutions With Respect to the Disagreement Point, J. Econ. Theory, 42, 50-58.