Efficient solutions to bargaining problems with uncertain disagreement points (original) (raw)

Rationality and the Nash Solution to Non-convex Bargaining Problems

Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implication of weaker versions of these two rationality conditions in the context of solutions to non-convex bargaining problems. It is shown that, together with the standard axioms of efficiency, anonymity and scale invariance, they characterize the Nash solution. This result makes a further connection between solutions to non-convex bargaining problems and rationalizability of choice functions in the theory of rational choice.

Relative Disagreement-Point Monotonicity of Bargaining Solutions

2003

Prominent bargaining solutions are disagreement-point monotonic. These solutions’ disagreement-point monotonicity ranking, on the other hand, is impossible to establish. In a large class of bargaining problems, however, a ranking of the relative disagreement-point monotonicity of these prominent bargaining solutions can be obtained. Using the ‘Constant Elasticity of Substitution’ class of bargaining problems, and regardless of the concavity of the Pareto frontier and of the increase in the disagreement point, we find that the Egalitarian solution is most monotonic with respect to changes in disagreement payoffs, followed by the Nash solution. The Equal Sacrifice solution turns out to be the least monotonic, followed by the Kalai/Smorodinsky solution. JEL classification number : C72.

Bargaining with endogenous disagreement: The extended Kalai–Smorodinsky solution

Games and Economic Behavior, 2012

Following Vartiainen we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome and a disagreement outcome: the disagreement outcome may serve as a reference point for the compromise outcome, but other interpretations are given as well. For this framework we propose and study an extension of the classical Kalai-Smorodinsky bargaining solution. We identify the (large) domain on which this solution is single-valued, and present two axiomatic characterizations on subsets of this domain.

person non-convex bargaining: Efficient proportional solutions

Operations Research Letters, 2010

For n-person bargaining problems the family of proportional solutions (introduced and characterized by Kalai) is generalized to bargaining problems with non-convex payoff sets. The so-called ''efficient proportional solutions'' are characterized axiomatically using natural extensions of the original axioms provided by Kalai. (M. Tvede).

Nash Bargaining Theory with Non-Convexity and Unique Solution

2009

We characterize a class of bargaining problems allowing for non-convexity on which all of Nash axioms except for that of symmetry uniquely characterize the asymmetric Nash bargaining solution. We show that under some basic conditions, the uniqueness of the solution is equivalent to the choice sets of the bargaining problems being “log-convex”. The well-recognized non-convex bargaining problems arising from duopolies with asymmetric constant marginal costs turn out to belong to this class. We compare the Nash bargaining solution with some of its extensions that appeared in the literature.

Bargaining among groups: an axiomatic viewpoint

International Journal of Game Theory, 2010

We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the "bargaining power" of a group is proportional to c α , where c is the cardinality of the group.

Single-Valued Nash Bargaining Solutions with Non-Convexity ∗

2018

We consider two-player bargaining problems with compact star-shaped choice sets arising from a class of economic environments. We characterize single-valued solutions satisfying the Nash axioms on this class of bargaining problems. Our results show that there are exactly two Nash solutions with each being a dictatorial (in favor of one player) selection of Nash product maximizers. We also provide an extensive form for implementing these two Nash solutions.

Monotonicity and equal-opportunity equivalence in bargaining

Mathematical Social Sciences, 2005

In this paper we study two-person bargaining problems represented by a space of alternatives, a status quo point, and the agents' preference relations on the alternatives. The notion of a family of increasing sets is introduced, which reflects a particular way of gradually expanding the set of alternatives. For any given family of increasing sets, we present a solution which is Pareto optimal and monotonic with respect to this family, that is, makes each agent weakly better off if the set of alternatives is expanded within this family. The solution may be viewed as an expression of equal-opportunity equivalence as defined in Thomson [19]. It is shown to be the unique solution that, in addition to Pareto optimality and the monotonicity property mentioned above, satisfies a uniqueness axiom and unchanged contour independence. A non-cooperative bargaining procedure is provided for which the unique backward induction outcome coincides with the solution. the participants at the XV Bielefeld FoG Meeting and two anonymous referees for their valuable suggestions and comments.

A Non­cooperative Solution to the Bargaining Problem

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.

Dynamics and axiomatics of the equal area bargaining solution

International Journal of Game Theory, 2000

We present an alternative formulation of the two-person equal area bargaining solution based on a dynamical process describing the disagreement point set. This alternative formulation provides an interpretation of the idea of equal concessions. Furthermore, it leads to an axiomatic characterization of the solution.