Efficiency-risk tradeoffs in dynamic oligopoly markets : with application to electricity markets

Abstract

In an abstract framework, we examine how a tradeoff between efficiency and risk arises in different dynamic oligopolistic markets. We consider a scenario where there is a reliable resource provider and agents which enter and exit the market following a random process. Self-interested and fully rational agents can both produce and consume the resource. They dynamically update their load scheduling decisions over a finite time horizon, under the constraint that the net resource consumption requirements are met before each individual's deadline. We first examine the system performance under the non-cooperative and cooperative market architectures, both under marginal production cost pricing of the resource. The statistics of the stationary aggregate demand processes induced by the two market architectures show that although the non-cooperative load scheduling scheme leads to an efficiency loss - widely known as the "price of anarchy" - the stationary distribution of the corresponding aggregate demand process has a smaller tail. This tail, which corresponds to rare and undesirable demand spikes, is important in many applications of interest. With a better understanding of the efficiency-risk tradeoff, we investigate, in a non-cooperative setup, how resource pricing can be used as a tool by the system operator to tradeoff between efficiency and risk. We further provide a convex characterization of the Pareto front of different system performance measures. The Pareto front determines the tradeoff among volatility suppression of concerned measurements in the system with load scheduling dynamics. This is the fundamental tradeoff in the sense that system performance achieved by any load scheduling strategies induced by any specific market architectures is bounded by this Pareto front.