Additive Rules for the Quasi-linear Bargaining Problem

By: Christopher P. Chambers and Jerry R. Green

Format:Print
| Language:English

Abstract

We study the class of additive rules for the quasi-linear bargaining problem introduced by Green. We provide a characterization of the class of all rules that are e¢ cient, translation invariant, additive, and continuous. We present several subfamilies of rules: the one parameter family of t-Shapley rules, the weighted coalitional rules, the simplicial cone rules, and the Steiner point rules. We discuss additional properties that solutions in these families possess. We discuss the relation of these solutions to the general class. The Steiner point rules satisfy more of our properties than any other class of rules. We also show that if there are at least three agents, any rule in the class we characterize violates the axiom of no advantageous reallocation.