Monotonicity and equal-opportunity equivalence in bargaining (original) (raw)

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.

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).

WPO, COV and IIA bargaining solutions for non-convex bargaining problems

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.

Monotonicity in bargaining networks

2010

We study bargaining networks, discussed in a recent paper of Kleinberg and Tardos , from the perspective of cooperative game theory. In particular we examine three solution concepts, the nucleolus, the core center and the core median. All solution concepts define unique solutions, so they provide testable predictions. We define a new monotonicity property that is a natural axiom of any bargaining game solution, and we prove that all three of them satisfy this monotonicity property. This is actually in contrast to the conventional wisdom for general cooperative games that monotonicity and the core condition (which is a basic property that all three of them satisfy) are incompatible with each other. Our proofs are based on a primal-dual argument (for the nucleolus) and on the FKG inequality (for the core center and the core median). We further observe some qualitative differences between the solution concepts. In particular, there are cases where a strict version of our monotonicity property is a natural axiom, but only the core center and the core median satisfy it. On the other hand, the nucleolus is easy to compute, whereas computing the core center or the core median is #P-hard (yet it can be approximated in polynomial time).

Twofold optimality of the relative utilitarian bargaining solution

Given a bargaining problem, the relative utilitarian (RU) solution maximizes the sum total of the bargainer's utilities, after having first renormalized each utility function to range from zero to one. We show that RU is 'optimal' in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of . Second, RU offers each person the maximum expected utility amongst all rescaling-invariant solutions, when it is applied to a random sequence of future bargaining problems generated using a certain class of distributions; this is recalls the results of and .

A non-cooperative interpretation of bargaining sets

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.

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.

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.

Preferences over Solutions to the Bargaining Problem

1997

There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, the authors find it useful to study preferences over solutions in their own right. They identify a set of appealing axioms on such preferences that lead to unanimity in the choice of solution, which turns out to