A nonzero-sum extension of Dynkin's stopping problem
Mathematics of Operations Research
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Mathematics of Operations Research
Correlated Equilibrium in Quitting Games
Mathematics of Operations Research
Continuous-Time Dynkin Games with Mixed Strategies
SIAM Journal on Control and Optimization
On the Starting and Stopping Problem: Application in Reversible Investments
Mathematics of Operations Research
Explicit Solution to an Optimal Switching Problem in the Two-Regime Case
SIAM Journal on Control and Optimization
Numerical Approximations for Nonzero-Sum Stochastic Differential Games
SIAM Journal on Control and Optimization
Optimal Stopping Games for Markov Processes
SIAM Journal on Control and Optimization
Optimal Stochastic Control and Carbon Price Formation
SIAM Journal on Control and Optimization
The Continuous Time Nonzero-Sum Dynkin Game Problem and Application in Game Options
SIAM Journal on Control and Optimization
Market Design for Emission Trading Schemes
SIAM Review
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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 non-zero-sum stochastic switching game with 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.