Computation of Sharp Bounds on the Expected Value of a Supermodular Function of Risks with Given Marginals

We show that the rearrangement algorithm (RA) introduced in Puccetti and Rüschendorf (2012 Puccetti, G., Rüschendorf, L. (2012). Computation of sharp bounds on the distribution of a function of dependent risks. Journal of Computational and Applied Mathematics 236(7):1833–1840.[Crossref], [Web of Science ®] , [Google Scholar]) to compute distributional bounds can be used also to compute sharp lower and upper bounds on the expected value of a supermodular function of d random variables having fixed marginal distributions. Compared to the analytical methods existing in the literature the algorithm is widely applicable, more easily obtained and gives insight into the dependence structures attaining the bounds.     

Correction of 'On the Inconsistency of Equilibrium Refinement'

Theory and Decision -     

The protection of atypical work in the Australian, British and German social security systems

It is a common feature of Australian, British and German social security law to exclude atypical work from many normal standards of protection. Social insurance and occupational welfare law still concentrate on the standard employment relationship, as they use length and continuity of employment as the major criteria for distributing benefits, and means-tested systems put those who depend on different sources of income, as most atypical workers do, at a disadvantage. However, equal treatment and even promotion are granted to one type of atypical work: the combination of domestic and atypical labour market work. Examples are the law of unemployment insurance in Great Britain and Germany, the family components within the social insurance schemes, the special British and Australian means-tested benefits for the working poor family, and parental leave legislation in Germany.     

E-Capacities and the Ellsberg Paradox

Ellsberg's (1961) famous paradox shows that decision-makers give events with known probabilities a higher weight in their outcome evaluation. In the same article, Ellsberg suggests a preference representation which has intuitive appeal but lacks an axiomatic foundation. Schmeidler (1989) and Gilboa (1987) provide an axiomatisation for expected utility with non-additive probabilities. This paper introduces E-capacities as a representation of beliefs which incorporates objective information about the probability of events. It can be shown that the Choquet integral of an E-capacity is the Ellsberg representation. The paper further explores properties of this representation of beliefs and provides an axiomatisation for them.     

A macroeconomic potential describing structural change of the economy

For the purpose of describing change in an economy's structure, and addressing issues of transformation, the notion of a time-dependent macroeconomic potential function is introduced. It penalizes deviations from equilibrium (entrepreneurial error) and induces moves toward equilibrium. Thus, from the concept of a potential function is derived the concept of short-term and long-term change forces. We focus here on the long-term structural changes of an economy as distinct from short-term cyclical variations, and we represent economic transformations as phase-transitions between monostable and ambiguous bistable states of the economy. One important feature of the potential function approach is that the parameter of the potential can be determined from empirical data. In particular, the parameters can be regressed for input variables. Hence, a relationship has been established between the structural change force and a set of input variables, some of which are controlled in part by either public or private sector agents. The method has been applied to West German and United States industry data for 1950–1980.     

Bargaining with Incomplete information an axiomatic approach

Within this paper we consider a model of Nash bargaining with incomplete information. In particular, we focus on fee games, which are a natural generalization of side payment games in the context of incomplete information. For a specific class of fee games we provide two axiomatic approaches in order to establish the Expected Contract Value, which is a version of the Nash bargaining solution.     

A model to support the assessment of subjective probabilities

Conclusions The purpose of this article has been to provide a new method for the determination of subjective probabilities. The kind of support which is suggested for the assessment process has several interesting properties. Constructed in accordance with the Savage theory the procedure considers a preference structure on the space of the possible actions A or on a suitably chosen space A ^* as its basis. This structure will be attained by pairwise comparison of the elements a _i A (or a _i ^*A ^*). It may be incomplete and inconsistent. A linear programming approach will use this information to derive numerical probabilities which are in accordance with the stated preference judgments. Therefore, it avoids the difficulties which arise when the judge has to assign the numerical values to the possible states of nature. On the other hand, this method presents the advantage of taking into consideration all relevant a priori information because of its systematic judgment process. Another important element is given by the use of coefficients which express the judge's confidence in the stated comparisons. Further relevance is added to the procedure by the relatively small consumption of time and work to report the judgments even in complex situations, and by the renunciation of any methodological knowledge on the part of the judges.This study was financed by a research grant of the Deutsche Forschungsgemeinschaft (DFG).