In this dissertation auction formats are developed and discussed that focus on three specific economic environments. Regarding the impossibility results from mechanism design, the main task for the implementation of auction designs is to balance allocative efficiency and incentive compatibility – the main characteristics a mechanism should provide. Therefore, the dissertation investigates the limits of conceivable relaxations of allocative efficiency and incentive compatibility for complex settings such as double auctions, interdependent-valuation environments and electricity market designs. The overall aim is to carefully weigh up the advantages and disadvantages for either relaxing allocative efficiency or respectively incentive compatibility.

Seit 2003 hat die Effizienzmessung im dynamischen Kontext erheblich an Aufmerksamkeit gewonnen. Die dynamische Effizienzanalyse berücksichtigt sowohl die zeitliche Interdependenz der Produktionsentscheidungen als auch Anpassungskosten. Zudem wird zwischen variablen und quasi-fixen Produktionsfaktoren unterschieden. Allerdings haben strukturelle dynamische Effizienzmodelle bisher Unsicherheit vernachlässigt, was zu irreführenden Effizienzwerten führen kann. Unsicherheit beeinflusst die optimale Anpassung von Produktionsentscheidungen; dies ist besonders relevant für die optimale Anpassung der quasi-fixen Faktoren im Zeitablauf. Deshalb ist es das Ziel dieser Doktorarbeit, diese Lücke zu schließen und ein theoretisches Modell für die dynamische Effizienzmessung unter Unsicherheit basierend auf einer Kostenminimierung zu entwickeln. Um ein solches Modell herzuleiten, verwendet die Autorin zwei Komponenten: den statischen Schattenkostenansatz und ein stochastisches duales Investitionsmodel unter Unsicherheit. Während der Schattenkostenansatz die ökonomische Effizienz in eine technische und eine allokative Komponente zerlegt, erlaubt das stochastische intertemporale Dualitätsmodell, Unsicherheit und Anpassungskosten zu berücksichtigen. Die resultierenden empirischen stochastischen Nachfragegleichungen dienen als Grundlage für die ökonometrische Schätzung der technischen und allokativen Effizienz. Die theoretischen Erkenntnisse des hergeleiteten Modells wurden anschließend mit Hilfe einer Simulation überprüft, mit dem Ziel, einerseits die Höhe der Verzerrung der geschätzten Koeffizienten durch ausgelassene Variablen zu ermitteln, wenn Unsicherheit bei der optimalen Faktoranpassung vernachlässigt wird, und andererseits den Einfluss der Unsicherheit auf die Faktornachfragegleichungen zu analysieren. Die Simulationsergebnisse zeigen, dass eine Vernachlässigung der Unsicherheit zur Verzerrung der geschätzten Modellparameter führt. / Since 2003, measuring efficiency in dynamic contexts has received considerable attention. Dynamic efficiency analysis accounts for both the interdependency of production decisions over time, as well as adjustment costs, and also distinguishes between variable and quasi-fixed inputs in the production process. However, structural models of dynamic efficiency have thus far ignored uncertainty; this may lead to misleading measures of efficiency. Uncertainty affects the optimal allocation of input decisions and it is particularly true for the optimal adjustment of quasi-fixed factors over time. Hence, to fill this gap, this thesis aims to develop a theoretical model of dynamic efficiency under uncertainty based on the cost-minimization problem. To derive such a model, the author uses two components, namely the static shadow cost approach and a stochastic dual model of investments under uncertainty. The shadow cost approach allows one to disentangle economic inefficiency into technical and allocative inefficiency, while the stochastic intertemporal duality model enables one to consider uncertainty and adjustment costs. Formulating an empirical model requires one to specify the functional form of the respective value function. Here, the specified value function properties facilitate output and price uncertainty to influence optimal factor demand equations. The resulting empirical stochastic factor demand equations then serve as a starting point for the econometric estimation of technical and allocative inefficiency measures. Theoretical findings from the derived model were subsequently tested using a simulation, to determine how large the omitted variable bias is on the estimates of the coefficients if uncertainty is ignored in optimal factor allocations, and to analyze the influence of uncertainty on factor demand equations. The simulation results reveal that disregarding uncertainty in optimal factor allocations leads to biased estimates of model parameters.

In this dissertation auction formats are developed and discussed that focus on three specific economic environments. Regarding the impossibility results from mechanism design, the main task for the implementation of auction designs is to balance allocative efficiency and incentive compatibility – the main characteristics a mechanism should provide. Therefore, the dissertation investigates the limits of conceivable relaxations of allocative efficiency and incentive compatibility for complex settings such as double auctions, interdependent-valuation environments and electricity market designs. The overall aim is to carefully weigh up the advantages and disadvantages for either relaxing allocative efficiency or respectively incentive compatibility.:Preface … 7 1. Introduction … 8 1.1. Applications of auction design … 8 1.2. Optimal use of information in allocation processes … 12 1.3. Modeling non-cooperative situations … 14 1.4. Motivation for the dissertation … 16 2. An Incentive Compatible Double Auction for Multi-Unit Markets with Heterogeneous Goods … 21 2.1. Introduction into double auctions … 21 2.2. Setting of a multi-unit market with heterogeneous goods … 25 2.3. Concept of the Incentive Compatible Double Auction (ICDA) … 29 2.4. Definition of the allocation rule … 31 2.5. Creation of the price vector and the trading bundles … 37 2.6. Characteristics of the Incentive Compatible Double Auction (ICDA) … 40 2.7. Discussion of the properties of the Incentive Compatible Double Auction (ICDA) … 43 3. An Alternating-Price Auction for Interdependent-Valuation Environments … 46 3.1. Introduction into ex-post efficient auction design … 46 3.2. Setting of an interdependent-valuation environment … 50 3.3. Concept of the Alternating-Price Auction (APA) … 54 3.4. Characteristics of the Alternating-Price Auction (APA) 62 3.5. Discussion of the properties of the Alternating-Price Auction (APA) … 64 4. Facilitating Short-Term and Long-Term Efficiency with an Integrated Electricity Market Design … 66 4.1. Introduction into electricity market designs … 66 4.2. Setting of an electricity market … 72 4.3. Concept of the Integrated Electricity Market Design (IEMD) … 78 4.4. Characteristics of the Integrated Electricity Market Design (IEMD) … 88 4.5. Discussion of the properties of the Integrated Electricity Market Design (IEMD) … 91 5. Conclusion ... 94 Reference List … 96