Implicit collusion and individual market power in electricity markets

Wholesale electricity markets may not produce competitive outcomes, either as a result of the exercise of market power, or through problems of implicit collusion. In comparison with the great amount of attention paid to issues of market power, the problems of implicit collusion have not been extensively studied. In this paper, we use a coevolutionary approach to explore the effect of the price elasticity of demand, capacity and forward contracts on implicit collusion in a duopoly. We will demonstrate that implicit collusion has the most importance in market conditions under which there is an intermediate amount of market power. Thus markets which are either highly competitive or in which one or both of the two generators can exercise considerable market power, are also markets in which implicitly collusive outcomes are less likely to arise.     

A model of market power and efficiency in private electronic exchanges

We investigate how private electronic markets (PEMs) can be used as a strategic tool by a large producer to compete against a consortium of smaller producers. We model the competition between a Large Producer and Consortium of producers in a two-tier supply chain as a game and characterize the resulting Subgame Perfect Nash Equilibrium. Our results demonstrate that as the costs of inputs to production increase, there are greater returns to ownership of a private exchange. Further, we demonstrate strong welfare enhancing effects of the PEM as the production efficiency of upstream suppliers declines. Finally, from a policy standpoint we show that when upstream suppliers are highly efficient, the creation of a private electronic exchange by the Large Producer will result in significant welfare loss.     

Pricing decisions for complementary products with firms’ different market powers

This article reports the results of a study that explores the pricing problems with regard to two complementary products in a supply chain with two manufacturers and one common retailer. The authors establish five pricing models under decentralized decision cases, including the MS-Bertrand, MS-Stackelberg, RS-Bertrand, RS-Stackelberg, and NG models, with consideration of different market power structures among channel members. By applying a game-theoretical approach, corresponding analytic solutions are obtained. Then, by comparing the maximum profits and optimal pricing decisions obtained in different decision cases, interesting and valuable managerial insights are established.     

Local smoothing estimates for some half-wave operators

In this paper we study the local smoothing estimates for some half-wave operators associated to nondegenerate convex hypersurfaces.     

Efficient algorithms for combined heat and power production planning under the deregulated electricity market

Combined heat and power (CHP) production is an important energy production technology that can yield much higher total energy efficiency than separate heat and power generation. In CHP production, the heat and power production follows a joint characteristic, which means that the production planning must be done in coordination. Cost-efficient operation of a CHP system can be planned by using an optimization model. A long-term planning model decomposes into thousands of hourly models. Earlier, in the regulated electric power market, the planning problem was symmetrically driven by heat and power demand. The liberalization of the power market has created an asymmetrical planning problem, where heat production responds to the demand and power production to the volatile market price. In this paper, we utilize this asymmetry to develop novel envelope-based dual algorithms for solving the hourly CHP models efficiently. The basic idea is to transform the three-dimensional characteristic operating region for heat and power production of each CHP plant into a two-dimensional envelope by taking the power price as a parameter. Then the envelopes of each plant are used for looking up the optimal solution rapidly. We propose two versions of the algorithm: the on-line envelope construction algorithm (ECON) where the envelopes are constructed for each hour based on the power price and the off-line envelope construction algorithm (ECOFF) where envelopes are pre-computed for all different power price ranges. We derive the theoretical time complexity of the two algorithms and compare their performance empirically with realistic test models against the ILOG CPLEX solver and the Power Simplex (PS) algorithm. PS is an extremely efficient specialized primal algorithm developed for the symmetrical CHP planning problem under the regulated market. On average, when reusing previous basic solutions, ECON is 603 times faster than CPLEX and 1.3 times faster than PS. ECOFF is 1860 times faster than CPLEX and four times faster than PS.     

The affine inflation market models

Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data.     

Spatial dependencies of wind power and interrelations with spot price dynamics

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. In particular, prices are more volatile due to the stochastic nature of wind, such that more generation of wind energy yields lower prices. Therefore, it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole. In this paper, we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas, incorporated into a supply and demand based model for the electricity spot price. This model is calibrated with German data. We find that the specific location of a turbine – i.e., its spatial dependence with respect to the aggregated wind power in the system – is of high relevance for its value. Many of the locations analyzed show an upper tail dependence that adversely impacts the market value. Therefore, a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases. This effect becomes more important for increasing levels of wind power penetration and may render the large-scale integration into markets more difficult.     

Firms can benefit from inaccurate market beliefs

A supplier sells to a retailer who serves a market with uncertain demand. Before the season starts, the retailer preorders from the supplier, who stocks to satisfy at least the preorder. After the actual demand is realized, the retailer can place an at-once order, which is satisfied up to stock availability. Market demand, as perceived by a firm, can differ from what it actually is. We find that a firm can benefit from holding an inaccurate market belief.     

Asymptotic theory of nonparametric regression estimates with censored data

For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right_censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, Cp and FPE criteria in the process of selecting the parameters.     

The Fast RODEO for Local Polynomial Regression

An open challenge in nonparametric regression is finding fast, computationally efficient approaches to estimating local bandwidths for large datasets, in particular in two or more dimensions. In the work presented here, we introduce a novel local bandwidth estimation procedure for local polynomial regression, which combines the greedy search of the regularization of the derivative expectation operator (RODEO) algorithm with linear binning. The result is a fast, computationally efficient algorithm, which we refer to as the fast RODEO. We motivate the development of our algorithm by using a novel scale-space approach to derive the RODEO. We conclude with a toy example and a real-world example using data from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite validation study, where we show the fast RODEO’s improvement in accuracy and computational speed over two other standard approaches.     

A Fast and Stable Updating Algorithm for Bivariate Nonparametric Curve Estimation

Abstract

An updating algorithm for bivariate local linear regression is proposed. Thereby, we assume a rectangular design and a polynomial kernel constrained to rectangular support as weight function. Results of univariate regression estimators are extended to the bivariate setting. The updates are performed in a way that most of the well-known numerical instabilities of a naive update implementation can be avoided. Some simulation results illustrate the properties of several algorithms with respect to computing time and numerical stability.     

Bootstrap approximation of nearest neighbor regression function estimates

Let (X, Y) be a random vector in the plane and denote by m(x) = (Y|X = x) the corresponding regression function. We show that the bootstrap approximation for the distribution of a smoothed nearest neighbor estimate of m(x) is valid. Also we compare, by Monte Carlo, confidence intervals which are obtained from both the normal and the bootstrap approximation.     

Equilibrium in semimonotone market games

This paper analyzes the existence of equilibrium for a class of market games in which agents are allowed to follow different patterns of behaviour, including cases where the strategy sets are neither compact nor convex. Agent’s behaviour is modelled in terms of “inverse reply correspondences” (mappings that associate to each agent’s strategy those outcomes that she finds acceptable). Sufficient conditions for an equilibrium to exist are provided     

Strong consistency of automatic kernel regression estimates

Regression function estimation from independent and identically distributed bounded data is considered. TheL ₂ error with integration with respect to the design measure is used as an error criterion. It is shown that the kernel regression estimate with an arbitrary random bandwidth is weakly and strongly consistent forall distributions whenever the random bandwidth is chosen from some deterministic interval whose upper and lower bounds satisfy the usual conditions used to prove consistency of the kernel estimate for deterministic bandwidths. Choosing discrete bandwidths by cross-validation allows to weaken the conditions on the bandwidths. Research supported by DAAD, NSERC and Alexander von Humboldt Foundation. The research of the second author was completed during his stay at the Technical University of Szczecin, Poland.     

Bilinear space-time estimates for linearised KP-type equations on the three-dimensional torus with applications

A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space-time estimates for this equation are obtained. Applications to the local and global well-posedness of dispersion generalised KP-II equations are discussed. Especially it is proved that the periodic boundary value problem for the original KP-II equation is locally well-posed for data in the anisotropic Sobolev spaces , if and ε>0.     

Visualization of competitive market structure by means of choice data

This paper presents a method for visualizing competitive market structures based on scanner panel data where asymmetries are taken into account. For this, I combined consumer choice models based on mixed logit models with three-mode principal component analysis. This approach can be used to unfold a competitive market structure map. The methodology presented is able to quantify the clout and receptivity of various brands. The results can then be visualized over time. Using this approach, guidelines for promotional activities of new brands can be provided, and possible threats from the competition detected.     

On the assortment optimization with endogenized market size

In this paper, we consider the joint effects of product substitution and market size endogenization. Under the substitution effects, a product’s demand may be cannibalized by other substitutable products; while the market size, measured by the number of customers who are interested in the products from the same category, may be largely influenced by the product offer set. We establish the computational complexity for the assortment problem under the joint effects, and develop a fully polynomial-time approximation scheme (FPTAS).     

Power and reversal power links for binary regressions: An application for motor insurance policyholders

In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of market power on risk-sharing

The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent’s set of strategic choices consists of the security payoffs and the pricing kernel that are consistent with the optimal-sharing rules; while in the incomplete setting, agents respond via demand functions on a vector of given tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium, the sharing securities are suboptimal, since agents submit for sharing different risk exposures than their true endowments. On the other hand, the Nash equilibrium prices stay unaffected by the game only in the special case of agents with the same risk aversion. In addition, agents with sufficiently lower risk aversion act as predatory traders, since they absorb utility surplus from the high risk averse agents and reduce the efficiency of sharing. The main results of the paper also hold under the generalized models that allow the presence of noise traders and heterogeneity in agents’ beliefs.