Bargaining with commitments

Mathematical Social Sciences, 2007

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 [Chae, S., Heidhues, P., 2004. A group bargaining solution. Mathematical Social Sciences 48, 37–53] and Vidal-Puga [Vidal-Puga, J.J., 2005a. A bargaining approach to the Owen value and the Nash solution with coalition structure. Economic Theory 25, 679–701]. Several axiomatic characterizations and two non-cooperative mechanisms are proposed.

International Journal of Game Theory, 2009

We introduce a new bargaining set for cooperative games in characteristic function form, and investigate its structure and properties. We prove that the new bargaining set is not empty. In fact, we show that it contains the kernel and is contained in the classical bargaining set M i 1 , and we further prove that it consists of the unique symmetric vector for the class of simple majority games. Keywords Cooperative game • Bargaining set • Reactive bargaining set • Kernel • Assignment game JEL Classification C71 Michael Maschler was intrigued by the reactive bargaining concept, which was introduced in my unpublished paper (Granot (1994)). Accordingly, in one of his many visits to UBC, he wanted to compare and contrast the outcomes and insights it provides with those provided by the kernel and the classical bargaining set for some well known examples considered in the literature, including the Five Person Market Game example he analyzed in his paper in JET, 1976, where he has demonstrated an advantage of the (classical) bargaining set over the core, and the Seven Person Projective Game, first introduced by von Neumann and Morgenstern. So, we set about to study these examples, and, as usual, the focus was expanded, resulting with our joint paper in IJGT in 1997. In view of the interest my unpublished paper has generated, and its relevance to Michael's work on the classical bargaining set and the kernel, I am delighted that a shorter version of it is appearing in an issue dedicated to Michael.

show that the Nash (1950) solution emerges as a limit point of a two player alternating o¤ers bargaining game when the time di¤erence between o¤ers goes to zero. establish the same result in the n¡player cake sharing set up. argue that noncooperative bargaining behavior á la Krishna-Serrano can be compactly described by means of von Neumann-Morgenstern stable set. This paper analyses the general problem. We show that a stable set exists and converges to the Nash solution in any smooth, compact and convex problem. A connection to the generalized Krishna-Serrano game is also established.

International Journal of Game Theory, 1995

European Journal of Operational Research, 2007

In this paper we study bargaining models where the agents consider several criteria to evaluate the results of the negotiation process. We propose a new solution concept for multicriteria bargaining games based on the distance to a utopian minimum level vector. This solution is a particular case of the class of the generalized leximin solutions and can be characterized as the solution of a finite sequence of minimax programming problems.

Journal of Mathematical Economics, 2010

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object's value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent. (JEL C73, C78, D44, D82, J12.

We present a simple mechanism of negotiation, based on offers and counteroffers. This leads to a unified solution theory for nontransferable utility (NTU) games that has as special cases the Nash bargaining solution for pure bargaining problems, the Shapley value for transfer utility (TU) games, and the Shapley NTU value for general cooperative games. These results are similar to those of the bargaining mechanism of Hart and yielding the consistent value Owen (1898, 1992)). The mechanism presented here solves some problematic issues in Hart and Mas-Colell's model. Furthermore, a natural extension to games with coalition structure, yielding the Owen value (Owen (1977)) for TU games is provided.

Homo Oeconomicus, 2016

We consider here pure bargaining problems endowed with a coalition structure such that each union is given its own utility. In this context we use the Shapley rule in order to assess the main options available to the agents: individual behavior, cooperative behavior, isolated unions behavior, and bargaining unions behavior. The latter two respectively recall the treatment given by Aumann-Drèze and Owen to cooperative games with a coalition structure. A numerical example illustrates the procedure. We provide criteria to compare any pair of behaviors for each agent, introduce and axiomatically characterize a modified Shapley rule, and determine its natural domain, that is, the set of problems where the bargaining unions behavior is the best option for all agents.

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.

2012

We consider an extension of strategic normal form games with a phase of negotiations before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, in order to provide additional incentives for each other to play designated strategies. Such offers are conditional on the recipients playing the specified strategies and they effect transformations of the payoff matrix of the game by accordingly transferring payoffs between players. We introduce and analyze solution concepts for 2-player normal form games with such preplay offers under various assumptions for the preplay negotiation phase and obtain results for existence of efficient negotiation strategies of the players. Then we extend the framework to coalitional preplay offers in N -player games, as well as to extensive form games with inter-play offers for side payments.