On arguments from self-interest for the Nash solution and the Kalai egalitarian solution to the bargaining problem

I argue in this paper that there are two considerations which govern the dynamics of a two-person bargaining game, viz. relative proportionate utility loss from conceding to one's opponent's proposal and relative non-proportionate utility loss from not conceding to one's opponent's proposal, if she were not to concede as well. The first consideration can adequately be captured by the information contained in vNM utilities. The second requires measures of utility which allow for an interpersonal comparison of utility differences. These considerations respectively provide for a justification of the Nash solution and the Kalai egalitarian solution. However, none of these solutions taken by themselves can provide for a full story of bargaining, since, if within a context of bargaining one such consideration is overriding, the solution which does not match this consideration will yield unreasonable results. I systematically present arguments to the effect that each justification from self-interest for respectively the Nash and the Kalai egalitarian solution is vulnerable to this kind of objection. I suggest that the search for an integrative model may be a promising line of research.I am grateful to Jon Elster, A. Hylland, F. Spinnewijn, J. Verhoeven and the members of the research group for theoretical sociology in the K.U.L. for their comments on an earlier version of this paper. I also thank the Ministry for Foreign Affairs (Norway) for its financial support and the members of the department of sociology in the University of Oslo for their hospitality and interest in my work.     

Risk aversion for losses and the Nash bargaining solution

Theory and Decision - We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in...     

Two simple characterizations of the Nash bargaining solution

We provide two alternative characterizations of the Nash bargaining solution. We introduce new simple axioms, strong undominatedness by the disagreement point, and egalitarian Pareto optimality. First, we prove that the Nash solution is characterized by symmetry, scale invariance, independence of irrelevant alternatives, and strong undominatedness by the disagreement point. Second, we replace the independence of irrelevant alternatives axiom with the sandwich axiom (Rachmilevitch in Theory Decis 80:427–442, 2016) and egalitarian Pareto optimality. We then demonstrate that the Nash solution is characterized by symmetry, scale invariance, strong undominatedness by the disagreement point, the sandwich axiom, and egalitarian Pareto optimality.     

Spatial bargaining in rectilinear facility location problem

Theory and Decision - We consider a spatial bargaining model where players collectively choose a facility location on a two-dimensional rectilinear distance space through bargaining using the...     

An extension of the Nash bargaining problem and the Nash social welfare function

This paper provides an extension of Nash's bargaining model. The extension permits the domain of a solution function to contain non-convex sets. First, it is shown that the proposed extension is a mathematical generalization of Nash's bargaining problem. Next, some relations between the extension and the Nash social welfare function are developed. The formal equivalence of the two constructs is demonstrated, and the intuitive significance of the results is discussed.I am indebted to S. Ishikawa for helpful comments on an earlier draft and to K. Nakamura for helpful discussions. Any errors that remain are of course my responsibility.     

Risk aversion and the relationship between Nash's solution and subgame perfect equilibrium of sequential bargaining

This article presents some new, intuitive derivations of several results in the bargaining literature. These new derivations clarify the relationships among these results and allow them to be understood in a unified way. These results concern the way in which the risk posture of the bargainers affects the outcome of bargaining as predicted by Nash's (axiomatic) solution of a static bargaining model (Nash, 1950) and by the subgame perfect equilibrium of the infinite horizon sequential bargaining game analyzed by Rubinstein (1982). The analogous, experimentally testable predictions for finite horizon sequential bargaining games are also presented.     

Lattices,bargaining and group decisions

This essay aims at constructing an abstract mathematical system which, when interpreted, serves to portray group-choices among alternatives that need not be quantifiable. The system in question is a complete distributive lattice, on which a class of non-negative real-valued homomorphisms is defined. Reinforced with appropriate axioms, this class becomes a convex distributive lattice. If this lattice is equipped with a suitable measure, and if the mentioned class of homomorphisms is equipped with a metric, then the class and its convex sets are seen to possess certain characteristic properties. The main result (Theorem 6) follows from a combination of these results and a famous result due to Choquet.The mathematical scheme is then interpreted in the subject-language of choice among alternatives. It is shown, by means of an example, that the system furnishes all the ingredients for describing multi-group choices. Whether or not the same ingredients are also adequate for a behavioural theory of multi-group choices is an issue that will not be gone into. However, the example effectively illustrates how a process of bargaining can be described with the aid of the mathematical scheme.In the second example, a class of bargaining situations is modelled in the symbolism of linear programming with several objective functions combined with unknown weights; the cost vectors in such formulations are identified with homomorphisms, and the main theorem of this essay is applied.     

Overlapping coalitions,bargaining and networks

We model the formation of coalitions that are not necessarily disjoint. We propose a new bargaining game that yields an overlapping coalition structure as an outcome. Equilibrium does not always exist in pure strategies for such a game, but we show that it always exists with a mild degree of mixed strategies. We derive conditions for a complete duality between networks and overlapping coalitions, and we provide a new rationale for the sequential formation of networks.     

Collective bargaining levels,employment and wage inequality in Spain

After the increase in inequalities following the Great Recession, studies on wage bargaining systems have increasingly focused on wage inequality. This research examines wage inequality associated with collective bargaining levels in Spain, based on matched employer–employee microdata and quantile regression methods. These methods are applied across the wage distribution, following the method proposed by Firpo et al. (2011), to estimate wage premiums associated with agreement levels and to decompose the wage differentials observed at different points of the wage distribution. From the evidence obtained it can be concluded that, although the higher wages found in firm-level agreements are explained by the better observed characteristics of firms and workers covered by these collective agreements, there remains a positive wage premium. Although this premium is seen throughout the wage distribution, it favours mostly workers in the middle and upper-middle end. This slightly increases wage inequality in comparison with sectoral agreements. In contrast, workers without collective bargaining coverage generally suffer a wage penalty. This penalty is only observed on the left of the wage distribution. It becomes a significant wage premium in the upper end of the distribution, which implies a significant increase in wage inequality. In short, the evidence of this research suggests that reducing the coverage of collective bargaining could be associated with a significant increase in wage inequality. A better policy option for countries with a predominant sectoral model, such as Spain, would be to move towards an organized decentralization model. This would cause significant gains in employment as suggested by OECD (2019) and only a slight increase in wage inequality.     

On the first-offer dilemma in bargaining and negotiations

Theory and Decision - In bargaining and negotiations, should one make the first offer or wait for the opponent to do so? Practitioners support the idea that moving first in bargaining is a mistake,...     

Distributive justice of bargaining and risk sensitivity

In this paper we will point out some possibilities and limitations of the discussion of distributive justice by bargaining in the classical bargaining models.We start by considering a kind of bargaining situation where two persons with different risk aversions have to distribute a given quantity of a certain good. Then we define a model in which two bargaining situations are compared. In both situations two persons divide a quantity of a certain good; in the second situation one of the persons, say person 2, is replaced by a more risk averse person. From a well-known theorem of Kihlstrom, Roth and Schmeidler it follows that in the Nash solution, the Kalai-Smorodinsky solution and the Maschler-Perles solution person 1 prefers the situation with the more risk averse opponent.In both classes of problems the judgement of distributive justice is impossible because of an informational poverty of the classical bargaining model. We propose to integrate changes in the economic situation of the persons into the model.Therefore, in a third step, we compare two distributive situations, where differences in the situations are implied by changes in the initial endowments of the persons. Under the assumption that each person has a decreasing local risk aversion, we show that every reallocation of the initial endowments is enlarged or at least preserved by risk sensitive bargaining solutions. This fact has some significance for the discussion of distributive justice in social decision making by bargaining.     

Interests and the Growth of Uncertainty

The sociology of knowledge and related work in social psychology have been biased towards overvaluing shared perspectives and the attainment of certainty. This paper moves to fill a theoretical gap created by relative inattention to the roles of nonshared perspectives and uncertainty by outlining a middle-range theory of the connections between human interests and uncertainty. It is proposed that individuals and groups find instrumental uses for uncertainty, just as they do for other states of mind, and that these uses arise from particular interests which characteristically belong to certain types of individuals or groups.     

Uncertainty,information and resolution of medical malpractice disputes

This study assesses the role of defendant liability in determining whether the plaintiff receives payment, relationship of compensation to economic loss, and stage of dispute resolution. An options pricing model explains how information acquired affects both decisions to drop or continue and settlement values, as well as the role of pecuniary motives for claiming. Cases in which a panel of physician evaluators thought defendant(s) to be innocent were much more likely to be dropped, as were cases in which innocence became more apparent as the case developed. Compensation was much less than economic loss on average. Questionable defendant liability meant reduced compensation.The research was supported in part by a grant from The Robert Wood Johnson Foundation entitled, Resolution of Malpractice Claims: Birth- and Emergency Room-Related Injuries (Grant No. 14045). We thank Mingliang Zhang, Lars Runquist, and Stephen van Wert for research assistance.     

The government, the market, and the problem of catastrophic loss

This article addresses the comparative advantage of the government to the private property/casualty insurance industry for the provision of insurance coverage for catastrophic losses. That the government can play an important role as an insurer of societal losses has been a central public policy principle since at least the New Deal. In addition, our government typically automatically provides forms of specific relief following unusually severe or unexpected disasters, which itself can be viewed as a form of ex post insurance. This article argues that, for systemic reasons, the government is much less effective than the private property/casualty insurance market in providing coverage of losses generally, but especially of losses in contexts of catastrophes.     

Relative acceptability: A proposed strategy for the bargaining game

Theory and Decision - In bargaining situations an actor faces a bifocal problem: He wants the best deal possible for himself, but unless his choice is coordinated with the antagonist's he is...     

Altruism,the free rider problem and group size

This paper is a survey of recent theoretical work on the influence of group size, perceived effectiveness or noticeability of one's behavior on a group member's altruistic responses. Experiments on this problem are analyzed and evaluated, and problems for future research are outlined.This paper is a revised version of a paper originally presented at the March 1973 meetings of the Public Choice Society. In preparing this paper I have benefited from criticisms and suggestions made by a number of people and I wish to take this opportunity to thank them. Among them are John Bonin, Barry Groffman, Bob O'Gorman, Don Moon, George Reynolds and Harrison Wagner.