The ordinal egalitarian bargaining solution for finite choice sets

Rubinstein et al. (Econometrica 60:1171–1186, 1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social choice problems using a new notion called the Ordinal Egalitarian (OE) bargaining solution. This suggests the middle ranked allocation (or a lottery over the two middle ranked allocations) of the Pareto set as an outcome. We show that the OE solution is characterized by weak credible optimality, ordinal symmetry and independence of redundant alternatives. We conclude by arguing that what allows us to make progress on this problem is that with finite choice sets, the counting metric is a natural and fully ordinal way to measure gains and losses to agents seeking to solve bargaining problems.     

Disagreement point monotonicity,transfer responsiveness,and the egalitarian bargaining solution

This paper provides an axiomatization of the egalitarian bargaining solution. The central axiom used (together with some standard properties of bargaining solutions) in this characterization is a transfer responsiveness condition. First, it ensures that no transfer paradox can occur if bargaining power is transferred from one agent to another by decreasing one agent's and increasing the other agent's component of the disagreement point. Second, the extent of external effects of such a transfer is limited by requiring that agents not involved in the transfer neither gain more than the winner nor lose more than the loser of the transfer. Journal of Economic Literature Classification No.: C78.I thank William Thomson whose comments on an earlier version led to substantial improvements.     

An axiomatization of the Nash bargaining solution

I prove that ‘Disagreement Point Convexity’ and ‘Midpoint Domination’ characterize the Nash bargaining solution on the class of two-player bargaining problems and on the class of smooth bargaining problems. I propose an example to show that these two axioms do not characterize the Nash bargaining solution on the class of bargaining problems with more than two players. I prove that the other solutions that satisfy these two properties are not lower hemi-continuous. These different results refine the analysis of Chun (Econ Lett 34:311–316, 1990). I also highlight a rather unexpected link with the result of Dagan et al. (Soc Choice Welfare 19:811–823, 2002).     

Police bargaining,arbitration, and fringe benefits

Data from a national sample of 500 to 600 U.S. cities with over 25,000 in population indicated that the practice of police collective bargaining has a positive, strong association with fringe benefits (measured by city contributions for police retirement and insurance benefits per police officer). The availability of arbitration, however, seems to have little or no influence on the dollar amount of police fringes, and neither the current nor the prior use of arbitration (i.e., actually receiving an arbitration award) has any consistent association with police fringes. The results indicate that collective bargaining and regional location influence the level of police fringes more than do other variables. We are grateful to Steve Kawakami, Mark Phillips, Joe Schimansky, and Dick Williams for some excellent research assistance. We are also grateful to the National Institute of Justice of the U.S. Department of Justice for financially supporting this research. Such support does not mean that the Institute or Department necessarily agrees with our methods or conclusions.     

The lexicographic egalitarian solution on economic environments

This paper considers solutions to distribution problems defined on economic environments. It shows that there is a unique resource-egalitarian and symmetric solution that proposes always Pareto optimal allocations and satisfies Inidivual Restricted Monotonicity; this property requires the poor people of the society to be strictly better-off when social resources increase and the initial outcome is a welfare unequal position. That unique solution is the lexicographic extension of the maxmin criterion.I wish to express my gratitude to Salvador Barberá. I am also very grateful to Hervé Moulin for his encouragement and to Carmen Herrero, Iñigo Iturbe and an anonymous referee for their suggestions. I thank very specially the valuable reading of John Roemer and illuminating conversations with Serge Christophe Kolm. Financial support from Gobierno de Navarra is gratefully acknowledged     

Distributive justice and the Nash bargaining solution

Suppes-Sen dominance or SS-proofness (SSP) is a commonly accepted criterion of impartiality in distributive justice. Mariotti (Review of Economic Studies, 66, 733–741, 1999) characterized the Nash bargaining solution using Nash’s (Econometrica, 18, 155–162, 1950) scale invariance (SI) axiom and SSP. In this article, we introduce equity dominance (E-dominance). Using the intersection of SS-dominance and E-dominance requirements, we obtain a weaker version of SSP (WSSP). In addition, we consider α ? SSP, where α measures the degree of minimum acceptable inequity aversion; α ? SSP is weaker than weak Pareto optimality (WPO) when α = 1. We then show that it is still possible to characterize the Nash solution using WSSP and SI only or using α -SSP, SI, and individual rationality (IR) only for any \({\alpha \in [0,1)}\). Using the union of SS-dominance and E-dominance requirements, we obtain a stronger version of SSP (SSSP). It turns out that there is no bargaining solution that satisfies SSSP and SI, but the Egalitarian solution turns out to be the unique solution satisfying SSSP.     

Weakest collective rationality and the Nash bargaining solution

We propose a new axiom, weakest collective rationality (WCR) which is weaker than both weak Pareto optimality (WPO) in Nash’s (Econometrica 18:155–162, 1950) original characterization and strong individual rationality (SIR) in Roth’s (Math Oper Res 2:64–65, 1977) characterization of the Nash bargaining solution. We then characterize the Nash solution by symmetry (SYM), scale invariance (SI), independence of irrelevant alternatives (IIA) and our weakest collective rationality (WCR) axiom.     

A characterization of the Nash bargaining solution

We characterize the Nash bargaining solution replacing the axiom of Independence of Irrelevant Alternatives with three independent axioms: Independence of Non-Individually Rational Alternatives, Twisting, and Disagreement Point Convexity. We give a non-cooperative bargaining interpretation to this last axiom. Received: 4 September 2000/Accepted: 6 September 2001     

Characterizing the Nash bargaining solution without Pareto-Optimality

We consider the bargaining problems with a variable number of agents. Lensberg had previously characterized the Nash solution as the only solution to satisfy the following axioms: Pareto-Optimality, Symmetry, Scale Invariance, and Multilateral Stability. We show that the disagreement solution is the only additional solution to satisfy the restricted list of axioms obtained by dropping Pareto-Optimality.Support from NSF under grant 8511136 is gratefully acknowledged. Thanks are also due to H. Moulin for his comments at an early stage of this research.     

A solution for two-person bargaining problems

Everyday bargaining problems are often solved by tossing a coin. A solution for two-person bargaining problems is axiomatized, which is a Pareto-optimal generalization of this coin tossing method. The super-additive solution of Perles and Maschler is also shown to be a generalization of this method. Various properties of our solution are studied, including continuity and risk sensitivity, and compared with properties of other solutions discussed in the literature.This study was financed by the Yrjö Jahnsson Foundation, which is gratefully acknowledged. I like to thank an anonymous referee for useful comments.     

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 Segal (J Polit Econ 108(3):569–589, 2000). 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 Harsanyi (J Polit Econ 61:434–435, 1953) and Karni (Econometrica 66(6):1405–1415, 1998).     

A universal meta bargaining implementation of the Nash solution

This paper follows van Damme (1986) in presenting a meta bargaining approach that justifies the Nash bargaining solution. But in contrast to van Damme's procedure our meta bargaining game is universal in the sense that all bargaining solutions are allowed as strategic choices in the meta bargaining game. Also our result holds true for any number n of players. Received: 31 July 2000/Accepted: 19 March 2001     

Omnibus or not: package bills and single-issue bills in a legislative bargaining game

Legislators sometimes pass unrelated issues in one bill with one vote (omnibus bills), but they often vote separately on different issues as well. In this article, a model is considered in which the first mover chooses whether to bargain over an omnibus bill or several separate bills. The main difference between the two types of bills is that trade-offs between issues are possible with omnibus bills, but not with separate bills. The underlying bargaining game is demand-bargaining (Morelli 1999). In this game, moderate legislators prefer to propose single-issue bills; extreme legislators prefer omnibus bills, if the asymmetry in policy ideal points in the legislature is large enough.     

Endogenous reference points and the adjusted proportional solution for bargaining problems with claims

 A modification of the proportional solution for bargaining problems with claims is proposed. This solution is constructed by considering an endogenous reference point. Characterization results of the aforementioned solution are provided. Received: 22 December 1993/Accepted: 12 August 1996     

Collective bargaining,compulsory arbitration,and salary settlements in the public sector: The case of New Jersey’s municipal police officers

This study investigates the effect of the use of final-offer arbitration on the salaries of municipal police officers in New Jersey using a regression model to control for the possible biases introduced by non-random use of the procedure. The results indicate that salary settlements which resulted from final-offer arbitration awards were not significantly higher or lower than conventionally arbitrated settlements or nonarbitrated settlements, despite the fact that arbitrators chose union final offers more frequently than they chose employer final offers. The results also contain evidence of asymmetric behavior by the parties under final-offer arbitration with the unions appearing more risk averse than the employers. An earlier version of this study was circulated under a different title as Working Paper No. 129 of the Industrial Relations Section, Princeton University. The author wishes to thank Joseph Altonji, Orley Ashenfelter, James Bennett, Gilles Grenier, Thomas Kochan, Richard Lester, John Pencavel, Jeffrey Tener, and an anonymous referee for their valuable comments on an earlier draft of this paper. The author also wishes to acknowledge the support for this study provided by the Center for New Jersey Affairs at Princeton University.     

Walking the talk in multiparty bargaining: An experimental investigation

We study the framing effects of communication on payoffs in multiparty bargaining. Communication has been shown to be more truthful and revealing than predicted in equilibrium. Because talk is preference-revealing, it may effectively frame bargaining around a logic of fairness or competition, moving parties on a path toward or away from equal-division agreements. These endogenous framing effects may outweigh any overall social utility effects due to the mere presence of communication. In two studies, we find that non-binding talk about fairness within a three-party, complete-information game leads toward off-equilibrium, equal division payoffs, while non-binding talk focusing on Competitive Reasoning moves parties away from equal divisions. Our two studies allow us to demonstrate that manipulated pre-game talk and spontaneous within-game dialogue lead to the same results.     

An economic analysis of public sector collective bargaining and strike activity

This paper develops a theory of public sector collective bargaining and uses it to investigate the economic determinants of public sector strike activity. The model considers union leaders, union members, bureaucrats, politicians, and voters, with the intention of explicitly recognizing both the constraints placed on the bargaining parties by their constituents and the differences between public and private sector collective bargaining. The empirical results indicate that only in cases where both negotiating parties are motivated by self-interest can we expect frequent strikes and strikes of long duration. The results also suggest that public sector strikes are countercyclical and principally influenced by the business cycle and its impact on state and local revenues.     

Nash implementation and the bargaining problem

We study Nash implementation of the bargaining solutions in a cake sharing set up. We argue that the minimal Pareto optimal, symmetric and Nash implementable SBS is the one inducing all Pareto optimal and midpoint-dominating utility vectors in each state.