Pricing bridges to cross a river.

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.Pricing; Networks; Tariffs; Costs; Cost; Demand; Problems; Order; Yield; Studies; Approximation; Algorithms; Performance;

Quadratic Regularization of Unit-Demand Envy-Free Pricing Problems and Application to Electricity Markets

We consider a profit-maximizing model for pricing contracts as an extension of the unit-demand envy-free pricing problem: customers aim to choose a contract maximizing their utility based on a reservation bill and multiple price coefficients (attributes). A classical approach supposes that the customers have deterministic utilities; then, the response of each customer is highly sensitive to price since it concentrates on the best offer. A second approach is to consider logit model to add a probabilistic behavior in the customers' choices. To circumvent the intrinsic instability of the former and the resolution difficulties of the latter, we introduce a quadratically regularized model of customer's response, which leads to a quadratic program under complementarity constraints (QPCC). This allows to robustify the deterministic model, while keeping a strong geometrical structure. In particular, we show that the customer's response is governed by a polyhedral complex, in which every polyhedral cell determines a set of contracts which is effectively chosen. Moreover, the deterministic model is recovered as a limit case of the regularized one. We exploit these geometrical properties to develop an efficient pivoting heuristic, which we compare with implicit or non-linear methods from bilevel programming. These results are illustrated by an application to the optimal pricing of electricity contracts on the French market.Comment: 37 pages, 9 figures; adding a section on the pricing of electricity contract

Estimating Network Effects and Compatibility in Mobile Telecommunications

This paper provides empirical evidence on the extent of network effects and compatibility between networks in mobile telecommunications. We specify a structural model of demand for mobile telephone service, which allows us to identify the parameters of interest from the S-shape of mobile service diffusion. The network effects are measured by the dependence of consumer willingness to pay on the installed base of subscribers. Compatibility is measured by the relative extent of cross- and own-network effects. As such, it indicates whether the network effects operate at the firm level, at the industry level, or at both. We then estimate this model for the Polish mobile telephone industry using quarterly panel data for the period 1996-2001. We find strong network effects, which give rise to upward-sloping demand, and, despite full interconnection of the mobile telephone networks, low compatibility. We show also that ignoring network effects in empirical models of emerging network industries might substantially bias downward the estimated price elasticity of demand. ZUSAMMENFASSUNG - (Schätzung von Netzwerkeffekten und Kompatibilität in Mobilfunktelekommunikation) Der vorliegende Beitrag bietet empirische Evidenz für den Umfang von Netzwerkeffekten und Netzwerkkompatibilität in der Mobilfunktelekom-munikation. Wir spezifizieren ein strukturelles Modell für die Nachfrage von Mobilfunkdienstleistungen, das die Parameter von Interesse mithilfe der S-förmigen Funktion der Dienstleistungsdiffusion identifiziert. Die Netzwerkeffekte werden durch die Abhängigkeit der Zahlungsbereitschaft der Konsumenten von der installierten Abonnentenbasis gemessen. Netzwerkkompatibilität wird durch den relativen Umfang der Quer- und Eigen-Netzwerkeffekte gemessen. Sie weist darauf hin, ob Netzwerkeffekten auf Unternehmensebene, auf Industrieebene, oder auf beiden Ebenen bestehen. Dann schätzen wir das Modell für die Polnische Mobilfunkindustrie mit vierteljährlichen Paneldaten für 1996-2001. Wir stellen starke Netzwerkeffekte fest, die eine positive Steigung in der Nachfragefunktion verursachen, und - trotz der technisch vollständigen Querverbindung der Mobilfunknetze - niedrige Kompatibilität. Wir zeigen auch, dass das Übersehen von Netzwerkeffekten in empirischen Modellen von neuen Netzwerkindustrien die geschätzte Preiselastizität der Nachfrage signifikant nach unten verzerren kann.Structural Econometric Model, Network Effects, Compatibility, Mobile Telecommunications

Pricing in Non-Convex Markets: How to Price Electricity in the Presence of Demand Response

A Walrasian competitive equilibrium defines a set of linear and anonymous prices where no coalition of market participants wants to deviate. Walrasian prices do not exist in non-convex markets in general, with electricity markets as an important real-world example. However, the availability of linear and anonymous prices is important for derivatives markets and as a signal for scarcity. Prior literature on electricity markets assumed price-inelastic demand and introduced numerous heuristics to compute linear and anonymous prices on electricity markets. At these prices market participants often make a loss. As a result, market operators provide out-of-market side-payments (so-called make-whole payments) to cover these losses. Make-whole payments dilute public price signals and are a significant concern in electricity markets. Besides, demand-side flexibility becomes increasingly important with growing levels of renewable energy sources. Demand response implies that different flexibility options come at different prices, and the proportion of price-sensitive demand that actively bids on power exchanges will further increase. We show that with price-inelastic demand there are simple pricing schemes that are individually rational (participants do not make a loss), clear the market, support an efficient solution and do not require make-whole payments. With the advent of demand-side bids, budget balanced prices (no subsidies are necessary) cannot exist anymore, and we propose a pricing rule that minimizes make-whole payments. We describe design desiderata that different pricing schemes satisfy and report results of experiments that evaluate the level of subsidies required for linear and anonymous prices on electricity spot markets with price-sensitive demand

A Classification Scheme for Local Energy Trading

The current trend towards more renewable and sustainable energy generation leads to an increased interest in new energy management systems and the concept of a smart grid. One important aspect of this is local energy trading, which is an extension of existing electricity markets by including prosumers, who are consumers also producing electricity. Prosumers having a surplus of energy may directly trade this surplus with other prosumers, which are currently in demand. In this paper, we present an overview of the literature in the area of local energy trading. In order to provide structure to the broad range of publications, we identify key characteristics, define the various settings, and cluster the considered literature along these characteristics. We identify three main research lines, each with a distinct setting and research question. We analyze and compare the settings, the used techniques, and the results and findings within each cluster and derive connections between the clusters. In addition, we identify important aspects, which up to now have to a large extent been neglected in the considered literature and highlight interesting research directions, and open problems for future work.Comment: 38 pages, 1 figure, This work has been submitted and accepted at OR Spectru

Other Markets, Other Costs: Modernizing Antitrust

Today’s antitrust law is characterized by stagnation and indeterminacy. The failure is so thorough that it is not clear that U.S. competition law actually leads to any outcomes that are defendable except at the most superficial level. Moreover, when enforcement does result in a desirable outcome, it not clear that it is the best outcome. The principal reason for this state of affairs is that antitrust scholars and courts cling to misguided goals and theories that have not evolved despite an avalanche of information now available that can modernize the discipline.This Article has two main sections that necessarily overlap. The first examines the three principal goals of antitrust — consumer surplus, allocative efficiency, and productive efficiency — and explains why they are imperfect, incomplete, and indeterminate guides for policy. The purpose of this section is not to express a nihilistic view of antitrust but to demonstrate that those who protect the status quo approach to antitrust stand on a wobbly foundation and to suggest that if the current rigidity in antitrust economics continues it will be at the expense of the relevancy of the discipline. It includes, sometimes by implication, proposals for improvement. The second section continues that basic theme but considers two areas in which growth is needed if antitrust is to remain relevant in the next fifty years. They may or may not be addressed but, if they are not, the legitimacy of antitrust economics and its application will surely be called into question. This material stresses the need, if there is to be a coherent antitrust policy, to broaden the scope of factors to consider when assessing the effectiveness of modern competition policy. The concluding section offers specific recommendations for the modernization of antitrust

A Dynamic Allocation Mechanism for Network Slicing as-a-Service

In my thesis, I explore the design of a market mechanism to socially efficiently allocate resources for network slicing as-a-Service. Network slicing is a novel usage concept for the upcoming 5G network standard, allowing for isolated and customized virtual networks to operate upon a larger, physical 5G network. By providing network slices as-a-Service, where the users of the network slice do not own any of the underlying resources, a larger range of use cases can be catered to. My market mechanism is a novel amalgamation of existing mechanism design solutions from economics, and the nascent computer science literature into the technical aspects of network slicing and underlying network virtualization concepts. The existing literature in computer science is focused on the operative aspects of network slicing, while economics literature is incompatible with the unique problems network slicing poses as a market. In this thesis, I bring these two strands of literature together to create a functional allocation mechanism for the network slice market. I successfully create this market mechanism in my thesis, which is split into three phases. The first phase allows for bidder input into the network slices they bid for, overcoming a trade-off between market efficiency and tractability, making truthful valuation Bayes-Nash optimal. The second phase allocates resources to bidders based on a modified VCG mechanism that forms the multiple, non-identical resources of the market into packages that are based on bidder Quality of Service demands. Allocation is optimized to be socially efficient. The third phase re-allocates vacant resources of entitled network slices according to a Generalized Second-Price auction, while allowing for the return of resources to these entitled network slices without service interruption. As a whole, the mechanism is designed to optimize the allocation of resources as much as possible to those users that create the greatest value out of them, and successfully does so