The Bargaining Set in Large Finite NTU Exchange Economies

Abstract

The bargaining set was originally defined by Aumann and Maschler [6]. Several different definitions have been subsequently proposed; the most frequently used definition was proposed by Davis and Maschler [8]. In the exchange economy context we consider here, the core consists of all allocations such that no coalition can propose an alternative set of trades which is feasible for the coalition on its own and which makes all of its members better off. All definitions of the bargaining set restrict the ability of coalitions to block (“object to”) an allocation, by taking into account the possibility that a second coalition might propose yet another set of trades (“counterobject”) and thereby cause some members to defect from the first coalition. In the Aumann-Maschler and Davis-Maschler definitions, the original objection is proposed by a single individual known as the leader of the objection; any counterobjecting coalition must exclude this leader. An objection is said to be justified if there is no counterobjection; the bargaining set consists of all allocations with no justified objection.

The author is grateful particularly to Walter Trockel, and in addition to Bob Aumann, Larry Ausubel, Truman Bewley, Don Brown, Gérard Debreu, Eddie Dekel-Tabak, Glenn Ellison, Drew Fudenberg, John Geanakoplos, Ted Groves, Bruce Hamilton, Walt Heller, Ehud Kalai, Edi Karni, Ali Khan, Michael Maschler, Eric Maskin, Andreu Mas-Colell, Roger Myerson, Wilhelm Neuefeind, David Pearce, Matthew Rabin, Debraj Ray, Arijit Sen, Chris Shannon, Max Stinchcombe, Rajiv Vohra, Akira Yamazaki, Bill Zame and Lin Zhou for helpful discussions.