A weak bargaining set for contract choice problems

2012

2005

In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues and . Several axiomatic characterizations and two noncooperative mechanisms are proposed.

Games and Economic Behavior, 1999

We show that the least core of a TU coalitional game with a finite set of players is contained in the Mas-Colell bargaining set. This result is extended to games with a measurable space of players in which the worth of the grand coalition is at least that of any other coalition in the game. As a consequence, we obtain an existence theorem for the Mas-Colell bargaining set in TU games with a measurable space of players.

Computational & Mathematical Organization Theory, 2005

In this paper we study the cooperative theory of stable outcomes for the roommates problem modeled as a contract choice problem. We show, that a simple generalization of the Deferred Acceptance Procedure with firms proposing due to , yields outcomes for a two-sided contract choice problem, which necessarily belong to the core and are Weakly Pareto Optimal for firms. Under additional assumptions : (a) given any two distinct workers, the set of yields achievable by a firm with the first worker is disjoint from the set of yields achievable by it with the second, and (b) the contract choice problem is pair-wise efficient, we prove that there is no stable outcome at which a firm can get more than what it gets at the unique outcome of our procedure.

International Journal of Game Theory, 2012

We characterize all n-person multi-valued bargaining solutions, defined on the domain of all finite bargaining problems, and satisfying Weak Pareto Optimality (WPO), Covariance (COV), and Independence of Irrelevant Alternatives (IIA). We show that these solutions are obtained by iteratively maximizing nonsymmetric Nash products and determining the final set of points by so-called LDR decompositions. If, next, we assume the (set-theoretic) Axiom of Determinacy, then this class coincides with the class of iterated Nash bargaining solutions; but if we assume the Axiom of Choice then we are able to construct an additional large set of discontinuous and even nonmeasurable solutions. We show however that none of these nonmeasurable solutions can be defined in terms of set theoretic formulae. We next show that a number of existing results in the literature as well as some new results are implied by our approach. These include a characterization of all WPO, COV and IIA solutions -including single-valued ones -on the domain of all compact bargaining problems, and an extension of a theorem of Birkhoff characterizing translation invariant and homogeneous orderings.

Review of Economic Design, 1999

This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional.

International Journal of Economic Theory

We give a notion of bargaining set for finite economies using Aubin's (1979) veto and show its coincidence with the set of Walrasian allocations, providing a discrete approach to the characterization of competitive equilibria obtained by Mas-Colell (1989) for continuum economies. We also study how the restriction on the formation of coalitions affects the bargaining set. In the last part of the work, using our equivalence result along with some known characterizations of Walrasian allocations, we state additional interpretations of the bargaining set.

Games and Economic Behavior, 2003

The cooperative solution concept introduced here, the demand bargaining set, contains the core and is included in the Zhou bargaining set, eliminating the "dominated" coalition structures. The demand vectors belonging to the demand bargaining set are self-stable. In the class of constant-sum homogeneous weighted majority games the demand bargaining set is non-empty and predicts a unique demand vector, namely a proportional distribution within minimal winning coalitions. The noncooperative implementation of the demand bargaining set is obtained for all the games that satisfy the one-stage property. Rajiv Vohra and the associate editor for helpful comments. Seminars at Cal.Tech., CORE, Brown, Harvard, Madison, Pompeu Fabra, Iowa State, and Stony Brook have been very helpful. The usual disclaimer applies.

Journal of Mathematical Economics, 2005

We introduce an extension of the Mas-Colell bargaining set and construct, by an elaboration on a voting paradox, a superadditive four-person nontransferable utility game whose extended bargaining set is empty. It is shown that this extension constitutes an upper hemicontinuous correspondence. We conclude that the Mas-Colell bargaining set of a non-levelled superadditive NTU game may be empty.

Games and Economic Behavior, 2003

The cooperative solution concept introduced here, the demand bargaining set, contains the core and is included in the Zhou bargaining set, eliminating the "dominated" coalition structures. The demand vectors belonging to the demand bargaining set are self-stable. In the class of constant-sum homogeneous weighted majority games the demand bargaining set is non-empty and predicts a unique demand vector, namely a proportional distribution within minimal winning coalitions. The noncooperative implementation of the demand bargaining set is obtained for all the games that satisfy the one-stage property. Rajiv Vohra and the associate editor for helpful comments. Seminars at Cal.Tech., CORE, Brown, Harvard, Madison, Pompeu Fabra, Iowa State, and Stony Brook have been very helpful. The usual disclaimer applies.