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We conclude this section by a discussion of the assumptions necessary in order to obtain existence of the symmetric equilibrium for the case of imperfect competition. While the assumption of linear demand does not seem to be essential in order to obtain our results, other assumptions made on the nature of uncertainty (the distribution of θ) and the set of available technologies k(c) are crucial. In particular we had to restrict the analysis to those d e n s i t i e s w h i c h d o n o t e x h i b i t u p w a r d s j u m p s , i . e . f 0 0 ( θ ) < 0 w h e n e v e r f 0 ( θ ) > 0 . T h reason is that if the distribution had high peaks, firms could want to deviate by “jumping on that peak” creating a situation where they are cheap and the others are relatively expensive just for those values of θ that have a high mass. We furthermore had to choose the e f r a m e w o r k s u c h t h a t e q u i l i b r i u m i n v e s t m e n t i s a c o n c a v e f u n c t i o n ( i . e . x 0 0 E Q ( c ) < 0 f o r a (c, c)). The reason is that the reaction of the opponents to more aggressive cost functions is driven by the steepness of their marginal cost functions. The steeper the marginal cost function of the opponents, the smaller their reaction. Notice that the requirement of concave equilibrium investment is closely related to continuity of the technology set k(c). That is, if only a discrete set of technologies is available, the resulting investment choice will be a step function which necessarily violates the above assumption. This implies however that an analysis of equilibrium cost functions under imperfect competition in the framework presented necessarily has to involve a continuous distribution of uncertainty and continuous technology sets. This seems to parallel the findings on supply function equilibria. In a seminal article Klemperer and Meyer (1989) show existence and uniqueness of differentiable supply functions for a continuous distribution of demand uncertainty. In a subsequent contribution Fehr and Harbord (1994) show, however, that those results do not hold for a discrete setting. l l c


Empirical Analysis for the German Electricity Mar- ket

In this section we demonstrate how our theoretical insights can be used to assess firms investment decisions in electricity generation facilities in liberalized electricity markets. Here, for the reason of data availability, we use data of the German electricity market. Our aim is to fit the theoretical model as closely as possible to the data of the German

e l e c t r i c i t y g e n e r a t i o n . A s i l l u s t r a t e d i n fi g u r e 7 , f o r t h e c a s e o f d u o p o l y ( X 2 E Q

) we do not observe over–

i n v e s t m e n t , w h e r e a s f o r t h e c a s e o f 4 s t r a t e g i c fi r m s ( X technologies. 2 E Q

) the model predicts over–investment in efficient


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