Merging and Going Bankrupt: A Neutral Solution

Alcalde, Jose and Marco-Gil, María del Carmen and Silva, José A. (2010): Merging and Going Bankrupt: A Neutral Solution.

Abstract

As it is known, there is no rule satisfying Additivity in the complete domain of bankruptcy problems. This paper proposes a notion of partial Additivity in this context, to be called m-additivity. We find that m-additivity, together with two quite compelling axioms, anonymity and continuity, identify the Minimal Overlap rule, introduced by Neill (1982).

• Item Type: MPRA Paper
• Language: English
• Keywords: Bankruptcy Problems; Additivity; Minimal Overlap Rule
• Subjects: D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

Alcalde, José, Maria del Carmen Marco and José A. Silva (2008): "The minimal overlap rule revisited," Social Choice and Welfare 31, 109-128.

Aumann, Robert J. and Michael Bahir Maschler (1985): "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory 36, 195-213.

Bergantiños, Gustavo and Luciano Méndez-Naya (2001): "Additivity in bankruptcy problems and in allocation problems," Spanish Economic Review 3, 223-229.

Chun, Youngsub and William Thomson (2005): "Convergence under replication of rules to adjudicate conflicting claims," Games and Economic Behavior 50, 129-142.

Moretti, Stefano and Fioravante Patrone (2008): "Transversality of the Shapley value," TOP 16, 1-41.

O'Neill, Barry (1982): "A problem of rights arbitration from the Talmud," Mathematical Social Sciences 2, 345-371.

Shapley, Lloyd S. (1953): "A value for n-person games," in: Kuhn, H., Tucker, A. (Eds.), Contributions to the Theory of Games, Vol. II. Princeton University Press, Princeton, NJ. volume 28 of Annals of Mathematics Studies, pp. 307-317.

Thomson, William (2003): "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences 45, 249-297.