Bargaining with nonanonymous disagreement: decomposable rules

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Kıbrıs, Özgür and Gürsel Tapkı, İpek (2011) Bargaining with nonanonymous disagreement: decomposable rules. Mathematical Social Sciences, 62 (3). pp. 151-161. ISSN 0165-4896

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Abstract

We analyze bargaining situations where the agents’ payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). We first show that this domain extension creates a very large number of new rules. Particularly, decomposable rules (which are extensions of rules from the Nash domain) constitute a nowhere dense subset of all possible rules. We next enquire if the counterparts of some standard results on the Nash (1950) domain continue to hold for decomposable rules on our extended domain. We first show that an extension of the Kalai-Smorodinsky bargaining rule uniquely satisfies the Kalai-Smorodinsky (1975)properties. This uniqueness result, however, turns out to be an exception. We characterize the uncountably large classes of decomposable rules that survive the Nash (1950), Kalai(1977), and Thomson (1981) properties. We also show that extensions to our domain of a standard independence property (by Peters, 1986) imply decomposability. Finally, we analyze the process through which “good” properties of rules on the Nash domain extend to ours.
Item Type: Article
Uncontrolled Keywords: disagreement matrix; axiomatic; dense; monotone path rule; proportional rule
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Arts and Social Sciences > Academic programs > Economics
Faculty of Arts and Social Sciences
Depositing User: Özgür Kıbrıs
Date Deposited: 30 Sep 2011 10:01
Last Modified: 28 Apr 2020 13:53
URI: https://research.sabanciuniv.edu/id/eprint/17030

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