An exact solution method for binary equilibrium problems with compensation and the power market uplift problem

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity

Recursive Sustainability: Intertemporal Efficiency and Equity

PV-optimality in a capital-resource economy can imply decreasing utility over some portion of the time horizon. Various criteria have been proposed to maintain intergenerational equity defined as nondeclining utility, but these have some limitations and problems. This paper proposes a new welfare criteria incorporating present value to maintain efficiency, and an equity function with convex costs on declining utility. This criterion is economically efficient, time-consistent and recursive. An extension of dynamic programming to multiple value functions is developed to solve this problem. Increasing the equity weight increasingly eliminates declining portions of utility time paths. Sustainability implies increasing consumption in the early time periods and some intermediate time periods relative to PV-optimality. A surprising result is that sustainability can actually result in increased resource usage in early time periods, followed later by higher levels of resource stocks compared to PV-optimality. The sustainability analysis shows that while conventional benefit-cost and valuation analysis contribute to efficiency, they do not necessarily induce sustainability due to incorrect dynamic GE prices. Similar comments apply to Green NNP analysis. The concepts and extended DP methods developed in this paper extend naturally to uncertainty and can also be applied to generalized consumer and social choice models beyond those typically considered in the literature.growth, environment, intergenerational equity, dynamic programming, Research Methods/ Statistical Methods,

Strong Duality for a Multiple-Good Monopolist

We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure $\mu$ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for $n$ independent uniform items each supported on $[c,c+1]$ is a grand-bundling mechanism, as long as $c$ is sufficiently large, extending Pavlov's result for $2$ items [Pavlov'11]. At the same time, our characterization also implies that, for all $c$ and for all sufficiently large $n$, the optimal mechanism for $n$ independent uniform items supported on $[c,c+1]$ is not a grand bundling mechanism

Emission Trading Systems and the Optimal Technology Mix

Cap and trade mechanisms enjoy increasing importance in environmental legislation worldwide. The most prominent example is probably given by the European Union Emission Trading System (EU ETS) designed to limit emissions of greenhouse gases, several other countries already have or are planning the introduction of such systems. One of the important aspects of designing cap and trade mechanisms is the possibility of competition authorities to grant emission permits for free. Free allocation of permits which is based on past output or past emissions can lead to inefficient production decisions of firms’ (compare for example B¨ohringer and Lange (2005), Rosendahl (2007), Mackenzie et al. (2008), Harstad and Eskeland (2010)). Current cap and trade systems grant free allocations based on installed production facilities, which lead to a distortion of firms’ investment incentives, however. It is the purpose of the present article to study the impact of a cap and trade mechanism on firms’ investment and production decisions and to analyze the optimal design of emission trading systems in such an environment

A Minimal Incentive-based Demand Response Program With Self Reported Baseline Mechanism

In this paper, we propose a novel incentive based Demand Response (DR) program with a self reported baseline mechanism. The System Operator (SO) managing the DR program recruits consumers or aggregators of DR resources. The recruited consumers are required to only report their baseline, which is the minimal information necessary for any DR program. During a DR event, a set of consumers, from this pool of recruited consumers, are randomly selected. The consumers are selected such that the required load reduction is delivered. The selected consumers, who reduce their load, are rewarded for their services and other recruited consumers, who deviate from their reported baseline, are penalized. The randomization in selection and penalty ensure that the baseline inflation is controlled. We also justify that the selection probability can be simultaneously used to control SO's cost. This allows the SO to design the mechanism such that its cost is almost optimal when there are no recruitment costs or at least significantly reduced otherwise. Finally, we also show that the proposed method of self-reported baseline outperforms other baseline estimation methods commonly used in practice

Option Pricing and Hedging with Small Transaction Costs

An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small transaction costs.Comment: 20 pages, to appear in "Mathematical Finance

The Optimal Inflation Rate in an Overlapping-Generations Economy with Land

This paper is concerned with the optimal inflation rate in an overlapping-generations economy in which (i) aggregate output is constrained by a standard neoclassical production function with diminishing marginal products for both capital and labor and (ii) the transaction-facilitating services of money are represented by means of a money-in-the-utility-function specification. With monetary injections provided by lump-sum transfers, the famous Chicago Rule prescription for monetary growth is necessary for Pareto optimality but a competitive equilibrium may fail to be Pareto optimal with that rule in force because of capital over accumulation. The latter possibility does not exist, however, if the economy includes an asset that is productive and non-reproducible--i.e., if the economy is one with land. As this conclusion is independent of the monetary aspects of the model, it is argued that the possibility of capital over accumulation should not be regarded as a matter of theoretical concern, even in the absence of government debt, intergenerational altruism, and social security systems or other "social contrivances."