Nash-equilibria in a heterogeneous oligopoly with fuzzy information

We consider a model of an oligopolistic market with heterogeneous firms and products where neither the cost nor the demand functions are common knowledge. Instead, each firm only has some vague ideas about the price strategies adopted by its competitors which is modelled by a fuzzy set. In analogy to the notion of an "equilibrium of actions and beliefs" we define and characterize a generalized Nash-equilibrium and show its existence under general conditions. Furthermore, the impact of the fuzzy information on the equilibrium outcome is analyzed by means of a comparative static analysis within a particular model framework.Received: 28 May 2002, Accepted: 25 December 2002, JEL Classification: D43, D80, L13We wish to thank Bernhard F. Arnold, the editor Murat Sertel , and two anonymous referees for helpful comments. Of course, we are responsible for all remaining errors.     

Competitive supply behavior when price information is fuzzy

The theory of fuzzy sets is applied to the output decisions of a price-taking firm facing imprecise information about expected future prices. Accepting risk resulting from the randomness of prices, the manager is interested in expected profits only. Since the set of possible expected-price vectors is fuzzy, a suitable defuzzification strategy is defined in analogy to the pessimism-optimism index proposed by L. Hurwicz. It depends on the manager's willingness to accept surprises resulting from a deviation of the true expected prices from the values that guided output decisions. Despite a linear cost function, well specified solutions to the optimization problem are possible without resorting to capacity constraints.     

An unexpected property of minimax estimation in the relative squared error approach to linear regression analysis

An unexpected property of the relative squared error approach to linear regression analysis is derived: It is shown that an estimator being minimax among all linear affine estimators is also minimax in the set of all estimators. Two illustrative special cases are mentioned, where a generalized least squares estimator and a general ridge or Kuks-Olman estimator turn out to be minimax.     

New Biotechnology Firms in Germany: Heidelberg and the BioRegion Rhine-Neckar Triangle

In Germany, in the second half of the nineties, a dynamic development of commercial biotechnology took place, undertaken by a considerable number of new firms. The following article deals with the foundation of biotechnological firms in the BioRegion Rhine-Neckar Triangle (with the center in Heidelberg). For a long time, the development of biotechnology in Germany and in the Rhine-Neckar Triangle was hindered by institutional barriers. The main reasons were the narrowing of company strategies of big chemical and pharmaceutical firms, the low impulses to found biotechnology companies out of academic research, the institutional surroundings not aligned to the needs of biotechnology (e.g. no venture capital market) and finally government restraints concerning the specific and particularly regional concentrated support of biotechnology. These particularities are also reflected by the structure of the population of young companies in the Rhine-Neckar Triangle. The main emphasis of biotechnology firms is placed on technological services (research on demand) and platform technologies, different sub-areas of therapeutics research (pharmaceutical basic materials, finding active substances), on the production for the diagnostics industry and on bioinformatics. These companies do not co-operate much, national and international relations predominate. Only a few scientists of regional research institutions want to found a biotechnology firm, although the region seems to attract a certain number of company founders from other regions.     

Partial Minimax Estimation in Regression Analysis

The general minimax estimator of the linear regression model is applicable when the whole parameter vector is restricted to an ellipsoid. In many applications, however, it is more realistic to assume that only a part of the parameter set is constrained. For this case an alternative minimax approach is developed.