Stochastic Switching Games and Duopolistic Competition in Emissions Markets

TL;DR

This paper models duopolistic competition in CO_2 emission markets as a stochastic switching game, analyzing equilibrium existence, strategies, and providing a simulation method for optimal decision-making.

Contribution

It introduces a novel stochastic switching game framework for emissions markets, establishing equilibrium existence and proposing a recursive solution approach.

Findings

Existence of Nash and correlated equilibria in the game.

Development of a simulation-based algorithm for equilibrium computation.

Numerical example demonstrating the model's application.

Abstract

We study optimal behavior of energy producers under a CO_2 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 reduced-form price-impact model for the CO_2 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.