Stochastic Switching Games and Duopolistic Competition in Emissions Markets

Abstract

We study optimal behavior of energy producers under a CO2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reducedform price-impact model for the CO2 allowance price. Such duopolistic competition results in a new type of a non-zero-sum stochastic switching game on finite horizon. Existence of game Nash equilibria is established through generalization to randomized switching strategies. No uniqueness is possible and we therefore consider a variety of correlated equilibrium mechanisms. We prove existence of correlated equilibrium points in switching games and give a recursive description of equilibrium game values. A simulation-based algorithm to solve for the game values is constructed and a numerical example is presented.2000 Mathematics Subject Classification. 91A15, 60G40, 93E20, 91B76.

On the equality of solutions of max–min and min–max systems of variational inequalities with interconnected bilateral obstacles

“…Switching problems have recently attracted a lot of research activities, especially in connection with mathematical finance, commodities, and in particular energy markets, etc (see e.g. [3,23,4,5,11,1,9,8,10,15,16,18,20,22,24,25,26,21,30,27,28] and the references therein). Several points of view, mainly dealing with control problems, have been considered (theoritical and practical [3,23,5,9,10,15,18,26], numerics [4,15], filtering and partial information [22]).…”

“…[3,23,4,5,11,1,9,8,10,15,16,18,20,22,24,25,26,21,30,27,28] and the references therein). Several points of view, mainly dealing with control problems, have been considered (theoritical and practical [3,23,5,9,10,15,18,26], numerics [4,15], filtering and partial information [22]). However, except [19,20], problems related to switching games did not attract that much interest in the literature.…”

A full balance sheet two-mode optimal switching problem

“…This class of switching problems and various extensions to multiple modes has recently attracted a lot of interest. In the following non-exhaustive list of references [2,25,4,3,14,1,10,9,12,18,17,20,24,27,26,30,21,35,31,34] the authors consider various aspects of the multiple modes switching problem, where only switching between the different modes is allowed until the end of the time horizon. Roughly, the setting assumes only that the state process, including the switching costs, are general processes adapted to the Brownian filtration.…”

The existence and uniqueness of a power price equilibrium

“…We do not focus on specific emission market schemes, but rather use a simplified version of it. For a detailed treatment of emission market in the game theoretic setting see [10] and [21].…”