Population-Monotonicity of the Nucleolus on a Class of Public Good Problems

Sonmez, Tayfun O. (2014): Population-Monotonicity of the Nucleolus on a Class of Public Good Problems.

Abstract

Sprumont (1990) shows that the Shapley value (Shapley 1957) is population-monotonic (Thomson 1983) on the class of convex games (Shapley 1971). In this paper we study the population-monotonicity of the nucleolus (Schmeidler 1969). We show that the nucleolus is not population-monotonic on the class of convex games. Our main result is that the nucleolus is population-monotonic on a class of public good problems which is formalized in Litilechild and Owen (1973) under the name of airport games. We also provide a recursive formula for the nucleolus of the airport game.

• Item Type: MPRA Paper
• Language: English
• Keywords: Population-monotonicity, airport game
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

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