Bargaining with endogenous disagreement: The extended Kalai–Smorodinsky solution (original) (raw)

The Kalai–Smorodinsky bargaining solution with loss aversion

Mathematical Social Sciences, 2011

We consider bargaining problems under the assumption that players are loss averse, i.e., experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on an outcome: an outcome z in a bargaining problem is self-supporting under a given bargaining solution, whenever transforming the problem using outcome z as a reference point, yields a transformed problem in which the solution is z.

Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions

Social Choice and Welfare, 2015

We reconsider the class of weighted Kalai-Smorodinsky solutions of Dubra (2001), and using methods of Imai (1983), extend their characterization to the domain of multilateral bargaining problems. Aside from standard axioms in the literature, this result involves a new property that weakens the axiom Bilateral Consistency (Lensberg, 1988), by making the notion of consistency dependent on how ideal values in a reduced problem change relative to the original problem.

Kalai-Smorodinsky Bargaining Solution Equilibria

Journal of Optimization Theory and Applications, 2010

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don't have an a-priori opinion on the relative importance of all these criteria. Roemer (2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution. We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered in Roemer (2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations such as the the extension to multicriteria games of the Selten's (1975) trembling hand perfect equilibrium concept.

Efficient solutions to bargaining problems with uncertain disagreement points

Social Choice and Welfare, 2002

We consider a cooperative model of bargaining where the location of the disagreement point may be uncertain. Based on the maximin criterion, we formulate an ex ante efficiency condition and characterize the class of bargaining solutions satisfying this axiom. These solutions are generalizations of the monotone path solutions. Adding individual rationality yields a subclass of these solutions. By employing maximin efficiency and an invariance property that implies individual rationality, a new axiomatization of the monotone path solutions is obtained. Furthermore, we show that an efficiency axiom employing the maximax criterion leads to an impossibility result.

Consistency, Replication Invariance, and Generalized Gini Bargaining Solutions

Journal of Economic Theory, 1996

On the basis of variable-population considerations, we characterize multi-valued bargaining solutions that are rationalized by special cases of the generalized Gini orderings. In addition to some fixed-population axioms, we use versions of the wellknown consistency principle to characterize the single-series Gini bargaining solutions and some of their subclasses (including the utilitarian solution). By adding a replication invariance condition, we provide a characterization of the single-parameter Gini solutions. Journal of Economic Literature Classification Number: C78.

Robustness of Intermediate Agreements and Bargaining Solutions

2009

Most real-life bargaining is resolved gradually. During this process parties reach intermediate agreements. These intermediate agreements serve as disagreement points in subsequent rounds. We identify robustness criteria which are satisfied by three prominent bargaining solutions, the Nash, Proportional (and as a special case to the Egalitarian solution) and Discrete Raiffa solutions. We show that the "robustness of intermediate agreements" plus additional well-known and plausible axioms, provide novel axiomatizations of the above-mentioned solutions. Hence, we provide a unified framework for comparing these solutions' bargaining theories.

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.