Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities

The (generalized) Gini indices rely on the social welfare function of a decision maker who behaves in accordance with Yaari's model, with a function f that transforms frequencies. This SWF can also be represented as the weighted sum of the welfare of all the possible coalitions in the society, where the welfare of a coalition is defined as the income of the worst-off member of that coalition. We provide a set of axioms (Ak) and prove that the three following statements are equivalent: (i) the decision maker respects (Ak), (ii) f is a polynomial of degree k, (iii) the weight of all coalitions with more than k members is equal to zero. Journal of Economic Literature Classification Number: D63.     

Non-Additive Beliefs and Strategic Equilibria

This paper studies n-player games where players' beliefs about their opponents' behaviour are modelled as non-additive probabilities. The concept of an “equilibrium under uncertainty” which is introduced in this paper extends the equilibrium notion of Dow and Werlang (1994, J. Econom. Theory64, 305–324) to n-player games in strategic form. Existence of such an equilibrium is demonstrated under usual conditions. For low degrees of ambiguity, equilibria under uncertainty approximate Nash equilibria. At the other extreme, with a low degree of confidence, maximin equilibria appear. Finally, robustness against a lack of confidence may be viewed as a refinement for Nash equilibria. Journal of Economic Literature Classification Numbers: C72, D81.     

Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods

We examine the effect of ambiguity in symmetric games with aggregate externalities. We find that ambiguity will increase/decrease the equilibrium strategy in games with strategic complements/substitutes and positive externalities. These effects are reversed in games with negative externalities. We consider some economic applications of these results to Cournot oligopoly, bargaining, macroeconomic coordination, and voluntary donations to a public good. In particular we show that ambiguity may reduce free-riding. Comparative statics analysis shows that increases in uncertainty will increase donations, to a public good. Journal of Economic Literature C72, D81, H41.     

金融经济领域中的不确定性研究综述

本文综述了Choquet容度和Choquet积分在刻画金融经济领域中不确定性上的应用,包含非期望效用、资产定价、保险理论、投资消费储蓄理论和宏观经济等五个方面,同时给出不确定性领域的进一步研究方向:动态相容性、理性、效用的合理定义以及非期望效用的推广等。     

A new integral for capacities

A new integral for capacities is introduced and characterized. It differs from the Choquet integral on non-convex capacities. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between the minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also in cases where the information available is limited to a few events. I wish to thank Eran Hanany, David Schmeidler, Eilon Solan and especially Yaron Azrieli and the anonymous referee of Economic Theory for their helpful comments.     

Foundations of neo-Bayesian statistics

We study an axiomatic model of preferences, which contains as special cases Subjective Expected Utility, Choquet Expected Utility, Maxmin and Maxmax Expected Utility and many other models. First, we give a complete characterization of the class of functionals representing these preferences. Then, we show that any such functional can be represented as a Choquet integral

where is the canonical mapping from the space of bounded Σ-measurable functions into the space of weak^*-continuous affine functions on a weak*-compact, convex set of probability measures on Σ. Conversely, any preference relation defined by means of such functionals satisfies the axioms of the model we study. Different properties of the capacity give rise to different models. Our result shows that the idea of Choquet integration is general enough to embrace all the models mentioned above. In doing so, it widens the range of applicability of well-known procedures in robust statistics theory such as the Neyman–Pearson lemma for capacities [P.J. Huber, V. Strassen, Minimax tests and the Neyman–Pearson lemma for capacities, Ann. Statist. 1 (1973) 251–263], Bayes' theorem for capacities [J.B. Kadane, L. Wasserman, Bayes' theorem for Choquet capacities, Ann. Statist. 18 (1990) 1328–1339] or of results like the Law of Large numbers for capacities [F. Maccheroni, M. Marinacci, A strong law of large numbers for capacities, Ann. Probab. 33 (2005) 1171–1178].     

谈判能力与标价策略

厂商能够通过策略性地选择不标价销售,利用其较强的谈判能力获取更多的利益。当厂商谈判能力较弱时,厂商将选择标价以最大化其利润。考虑消费者的谈判成本,厂商选择不标价时,其利润和谈判能力呈倒U型关系。当厂商谈判能力过高时,由于消费者将无利可图而放弃购买,因而厂商将选择标价的策略。在一定条件下,厂商实施策略性不标价不是市场有效的,可以通过强制标价实现市场的有效性。     

Allies or commitment devices? A model of appointments to the Federal Reserve

We present a model of executive‐legislative bargaining over appointments to independent central banks in the face of an uncertain economy with strategic economic actors. The model highlights the contrast between two idealized views of Federal Reserve appointments. In one view, politicians prefer to appoint conservatively biased central bankers to overcome credible commitment problems that arise in monetary policy. In the other, politicians prefer to appoint allies, and appointments are well described by the spatial model used to describe appointments to other agencies. Both ideals are limiting cases of our model, which depend on the level of economic uncertainty. When economic uncertainty is extremely low, politicians prefer very conservative appointments. When economic uncertainty increases, politicians’ prefer central bank appointees closer to their own ideal points. In the typical case, the results are somewhere in between: equilibrium appointments move in the direction of politician's preferences but with a moderate conservative bias.     

An Experimental Study of the Effect of Private Information in the Coase Theorem

We investigate, in an experimental setting, the effect of private information on the Coase theorem's predictions of efficiency and allocative neutrality. For a two-person bargaining game, we find significantly more inefficiency and allocative bias in the case of private information compared with the case of complete information. We also find substantial bargaining breakdown, which is not predicted by the Coase theorem. For the case of private information, we reject the Coase theorem in favor of the alternative of a generalized version of the Myerson—Satterthwaite theorem, which predicts inefficiency, allocative bias in the direction of the disagreement point, and some bargaining breakdown.     

WAGE AND EMPLOYMENT DETERMINATION THROUGH NON-COOPERATIVE BARGAINING

This paper investigates wage and employment determination by a group of workers or union and a firm, making use of the techniques of non-cooperative bargaining. Previous analyses have examined wage determination with an artificial restriction that employment is determined either before or after wage determination has occurred. Here, employment determination is made part of the bargaining process. With two variables being determined, there is bargaining with a variable pie and solutions correspond to equilibria without commitment. Two different notions of efficiency – exchange and pie efficiency – are relevant and serve to characterise equilibria. Multiple equilibria are shown to arise naturally once exchange inefficient proposals are possible. In all equilibria there is overemployment. Factors that restrict a firm's ability to alter the labour force during or after the wage-bargaining process are shown, paradoxically, to benefit the firm.     

Gamson's Law versus non-cooperative bargaining theory

We compare Gamson's Law, a popular empirical model of legislative bargaining, with two non-cooperative bargaining models in three players divide the dollar games in which no player has enough votes to form a winning coalition on their own. Both of the game theoretic models better organize the comparative static data resulting from changes in nominal bargaining power than does Gamson's Law. We also identify deviations from the point predictions of the non-cooperative bargaining models. Namely, proposer power is not nearly as strong as predicted under the Baron–Ferejohn model, and a significant number of bargaining rounds tend to take more than two steps under demand bargaining and more than one stage under Baron–Ferejohn, counter to the models' predictions. Regressions using the experimental data provide results similar to the field data, but fail to do so once one accounts for predictions regarding coalition composition under Gamson's Law.     

Half empty, half full and why we can agree to disagree forever

Aumann [Aumann R., 1976. Agreeing to disagree. Annals of Statisitics 4, 1236–1239] derives his famous we cannot agree to disagree result under the assumption that people are expected utility (=EU) decision makers. Motivated by empirical evidence against EU theory, we study the possibility of agreeing to disagree within the framework of Choquet expected utility (=CEU) theory which generalizes EU theory by allowing for ambiguous beliefs. As our first main contribution, we show that people may well agree to disagree if their Bayesian updating of ambiguous beliefs is psychologically biased in our sense. Remarkably, this finding holds regardless of whether people with identical priors apply the same psychologically biased Bayesian update rule or not. As our second main contribution, we develop a formal model of Bayesian learning under ambiguity. As a key feature of our approach the posterior subjective beliefs do, in general, not converge to “true” probabilities which is in line with psychological evidence against converging learning behavior. This finding thus formally establishes that CEU decision makers may even agree to disagree in the long-run despite the fact that they always received the same information.     

Monitoring Wage Developments in EMU

The purpose of this paper is to provide a brief review of aggregatewage developments in the EU member states. We start with a short discussion of wage bargaining mechanisms, their impact on labour market outcomes, and take a look into the crystal ball to learn about possible future developments. Section III analyses nominal wage developments focussing, in particular, on the evolution of cross-country patterns as anindicator for the synchronisation of wage developments. Section IV discusses real wage growth in relation to productivity developments using a somewhat refined 'real wage gap indicator';and Section V simply concludes.     

Incomplete Enforcement of Pollution Regulation: Bargaining Power of Chinese Factories

Only a limited number of papers haveempirically examined the determinants of themonitoring and enforcement activities performedby the environmental regulator. Moreover, mostof these studies have taken place in thecontext of developed countries. In this paper,we empirically examine the determinants of theenforcement of pollution charges in China.More precisely, we seek to identify thecharacteristics which may give firms more orless bargaining power with local environmentalauthorities pertaining to the enforcement(collection) of pollution charges. Firms fromthe private sector appear to have lessbargaining power than state-owned enterprises.Firms facing an adverse financial situationalso appear to have more bargaining power.Finally, we also show that the higher thesocial impact of a firm's emissions (asmeasured by the presence of complaints), thesmaller the bargaining power of the firms withlocal environmental authorities.