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).     

Why do larger families reduce parental investments in child quality, but not child quality per se?

Becker’s Quantity–Quality model (Becker in Demographic and economic change in developed countries, Princeton University Press, Princeton, pp 209–240, 1960; Becker and Lewis in J Polit Econ 81(2): S279–S288, 1973; Becker and Tomes in J Polit Econ 84(4): S143–S162, 1976) suggests a trade-off between family size and parental investments in children. To date, only Cáceras-Delpiano (J Hum Resour 41(4): 738–754, 2006) tests this theory by considering private school enrolment. This study extends this work by using a unique data set containing a broader range of parental investments that are arguably linked to parental intentions for producing higher quality children, such as overall and non-sectarian private school enrolment, the number of computers in the home per child, and saving for the child’s education. Both studies find that fertility reduces parental investments. However, the literature generally finds that fertility has no impact on child outcomes. The study offers three potential explanations for this ‘puzzle’.     

Minimum winning versus oversized coalitions in public finance: the role of uncertainty

This paper extends Persson et al.’s (J Polit Econ 108:1121–1161, 2000) simple legislature in the context of public finance with certainty to uncertainty. In our uncertain world, oversized coalitions (OSCs) as well as minimum winning coalitions (MWCs) may arise in equilibrium, and the agenda setter’s proposed policy may fail to receive a majority support. This is in marked contrast to the certain world, in which only MWCs can arise in equilibrium and the agenda setter’s proposal never fails to pass. When OSCs arise, we show that both public good provision and redistribution are likely to achieve their first-best solution, even if the legislature is simple.     

Cohabitation Premium in Men’s Earnings: Testing the Joint Human Capital Hypothesis

This paper provides new evidence on the increase in wage earnings for men due to marriage and cohabitation (in the literature, commonly referred to as marital and cohabitation wage premiums for men). Using data for a sample of white men from the National Longitudinal Survey of Youth 1979, the paper shows that even after accounting for potential selection bias there is a cohabitation wage premium for men, albeit smaller than the marriage premium. Our analysis shows that a joint human capital hypothesis (a la Benham in J Polit Econ 82(2, Part 2):S57–71, 1974) with intra-household spillover effects of partner’s education can explain the existence of the wage premiums. Our estimates provide some empirical support for the joint human capital hypothesis.     

Welfarist evaluations of decision rules for boards of representatives

We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to Barberà and Jackson (J Polit Econ 114(2):317–339, 2006) and to Banzhaf voting power.     

Sequential entry in many-to-one matching markets

We study sequential bargaining in many-to-one matching markets. We show that there is an advantage to entering late in the market, and that the last agent to enter the market will receive his or her best partner in a stable matching, extending the results of Blum and Rothblum (J Econ Theory 103(2):429–443, 2002) and Cechlárová (Randomized matching mechanism revisited. Mimeo, Safarik University, 2002) for the marriage model. We also discuss the relation between sequential bargaining and a possible alternative formulation based on the NTU Shapley value. We thank Peter Biró and Utku ünver for their advice on the related literature. We also thank an anonymous referee for comments.     

A note on the structure of stochastic social choice functions

This note sharpens the result of Nandeibam (J Econ Theory 68:212–233, 1996). We show that a stochastic social choice function which satisfies regularity, independence of irrelevant alternatives and weak ex-post Pareto optimality is essentially a weak random dictatorship.     

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1.     

Reconsidering two-agent Nash implementation

In this paper, we reconsider the full characterization of two-agent Nash implementation provided in the celebrated papers by Moore and Repullo (Econometrica 58:1083–1099, 1990) and Dutta and Sen (Rev Econ Stud 58:121–128, 1991), since we are able to show that the characterizing conditions are not logically independent. We prove that an amended version of the conditions proposed in these papers is still necessary and sufficient for Nash implementability. Then, by using our necessary and sufficient condition, we show that Maskin’s impossibility result can be avoided under restrictions on the outcomes and the domain of preferences much weaker than those previously imposed by Moore and Repullo (Econometrica 58:1083–1099, 1990) and Dutta and Sen (Rev Econ Stud 58:121–128, 1991).     

Generalized stochastic dominance and bad outcome aversion

Incomplete preferences over lotteries on a finite set of alternatives satisfying, besides independence and continuity, a property called bad outcome aversion are considered. These preferences are characterized in terms of their specific multi-expected utility representations (cf. Dubra et al., J Econ Theory, 115:118–133, 2004), and can be seen as generalized stochastic dominance preferences.     

A characterization of prudent choices

We define and axiomatize prudent choices for two criteria. Given two criteria, the alternatives chosen by the prudent choice procedure are the ones maximizing some composition of the criteria. This composition is such that (1) it contains the first criterion and a part of the second one, and (2) the new binary relation is not cyclic and cannot be enlarged with preferences of the second criterion without becoming cyclic. We also make the link between prudent choices, classical rational choices, sequentially rational choices (Manzini and Mariotti in Am Econ Rev 97(5):1824–1839, 2007a) and lexicographic binary choice rational choices (Tadenuma in J Econ Theory 104(2):462–472, 2002).     

Reference functions and possibility theorems for cardinal social choice problems

 In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions. Received: 8 August 1994/Accepted: 12 February 1996     

Constructing indices of multivariate polarization

Multivariate indices of polarization are constructed to measure effects of non-income attributes like wealth and education. Polarization is considered as the presence of groups which are internally homogeneous, externally heterogeneous, and of similar size. We propose a class of polarization indices which is built from measures of relative groups size and from decomposable indices of socio-economic inequality. For the latter, we employ the special inequality indices of Maasoumi (Econometrica 54:991–997, 1986), Tsui (J Econ Theory 67:251–265, 1995; Soc Choice Welf 16:145–157, 1999) and Koshevoy and Mosler (J Multivar Anal 60:252–276, 1997). Then, postulates for multidimensional polarization measurement are stated and discussed. The approach is illustrated by an empirical application to the population of the East and West Germany with polarization defined on income and education.     

Erratum to: Equivalence scales,the cost of children and household consumption patterns in Italy

This article deals with the estimation of parametric equivalence scales for Italian households with different demographic characteristics: composition, location and number of employed members in the household. Using a sample of 43,701 observations on monthly current expenditures from 1997 to 2004 we estimate a demand system for ten goods and we tackle the problem of corner solutions for some goods adopting the Two Step estimator proposed by Shonkweiler and Yen (Am J Agric Econ 81:972–982, 1999). The consumption behavior of households is also analyzed calculating compensated, uncompensated and expenditure elasticites for each commodity. By considering households that differ in composition (number of children), geographic location (four-different macro-areas of Italy), and number of employed adults, we allow for a range of useful comparisons.     

Two simplified proofs for Roberts’ theorem

Roberts (Aggregation and Revelation of Preferences. Papers presented at the 1st European Summer Workshop of the Econometric Society, pp. 321–349. North-Holland, 1979) showed that every social choice function that is ex-post implementable in private value settings must be weighted VCG, i.e. it maximizes the weighted social welfare. This paper provides two simplified proofs for this. The first proof uses the same underlying key-point, but significantly simplifies the technical construction around it, thus helps to shed light on it. The second proof builds on monotonicity conditions identified by Rochet (J Math Econ 16:191–200, 1987) and Bikhchandani et al. (Econometrica 74(4):1109–1132, 2006). This proof is for a weaker statement that assumes an additional condition of “player decisiveness”. Supported by grants from the Israeli Ministry of Science and the Israeli Academy of Sciences.     

Discrete choice models of labour supply,behavioural microsimulation and the Spanish tax reforms

The aim of the present study is to show the potential of behavioural microsimulation models as powerful tools for the ex ante evaluation of public policies. We analyse the impact of recent Spanish income tax reforms upon efficiency and household and social welfare and study the effects of various (basic-income and vital-minimum) flat tax schemes. The analysis is performed using a microsimulation model in which labour supply is explicitly taken into account. Instead of following the traditional continuous approach (Hausman, Labour supply, Aaron and Pechman (eds.), How Taxes Affect Economic Behaviour, The Brooking Institution, Washington, DC, 1981; Econometrica, 53: 1255–1282, 1985; Taxes and labour supply, Auerbach and Feldstein, (eds.), Handbook of Public Economics, North-Holland, Amsterdam, vol. 1, 1979), we estimate the direct utility function employing the methodology proposed by Aaberge et al. (Scand. J. Econ., 97: 635–659, 1995) and Van Soest (J. Hum. Resour., 30: 63–88, 1995). We maintain population heterogeneity by applying a social welfare analysis to the complete sample, rather than merely focusing on the active population. The source of our data is a sample of Spanish individuals in the 1995 wave of the EC Household Panel. We find that the redistribution policies considered have only had a minor impact on economic efficiency but, by contrast, have significantly affected social welfare. An erratum to this article can be found at     

Gamson’s law and hedonic games

This note adds one celebrated coalition formation game due to Gamson (Am Soc Rev 26:373–382 1961a, Am Soc Rev 26:565–573, 1961b) in the list of applications of the theory of hedonic games explored by Banerjee et al. (Soc Choice Welf 18:135–153, 2001) and Bogomolnaia and Jackson (Games Econ Behav 38: 204–230, 2002). We apply their results to study the original Gamson game and offer extensions both to a multi-dimensional characteristics space and to an infinite number of players.     

On the selection of the same winner by all scoring rules

Different scoring rules can result in the selection of any of the k competing candidates, given the same preference profile, (Saari DG 2001, Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence, R.I.). It is also possible that a candidate, and even a Condorcet winning candidate, cannot be selected by any scoring rule, (Saari DG 2000 Econ Theory 15:55–101). These findings are balanced by Saari’s result (Saari DG 1992 Soc Choice Welf 9(4):277–306) that specifies the necessary and sufficient condition for the selection of the same candidate by all scoring rules. This condition is, however, indirect. We provide a sufficient condition that is stated directly in terms of the preference profile; therefore, its testability does not require the verdict of any voting rule.     

Collective labor supply with many consumption goods

We extend Chiappori??s (J Polit Econ 100:437?C467, 1992) standard, ??collective?? model of labor supply to the case of several consumption goods. We show that more robust estimates obtain. Moreover, individual demands for each commodity, although unobservable, can be recovered up to an additive constant. In particular, the impact of changes in wages, non labor income or distribution factors on individual consumption patterns can be identified even though no individual consumption is observed.     

Top-Pair and Top-Triple Monotonicity

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.