A Game Theoretical Approach to Cap and Trade System Modeling and Auction Design

Abstract

The UN Environmental Program’s Emissions Gap Report, prepared by 44 scientific organizations in 17 countries, proclaimed that global temperatures will increase by a staggering 3.2°C until 2100 at the current rate of carbon emissions. The committee corroborated a previous report urging nations to take action before 2020 to bound the temperature increase to 1.5°C. Despite numerous forewarnings, corporations and individuals have failed to meaningfully adjust their behavior. This paper examines one potentially promising program to abate global warming referred to as “cap and trade,” a system in which the government sets an upper limit on annual carbon emissions levels and either issues or auctions tradable allowances to regulated firms. The program relies on market behavior to incentivize firms to reduce their emissions to avoid the cost of allowances, or to pay their fair share of the social costs of greenhouse emissions if they do not take steps to reduce their pollution. This study utilized multiple approaches to consider and analyze designs for cap and trade systems. We qualitatively examined designs of cap and trade programs that have been implemented by governments, and then reduced the key design decisions of a cap and trade system, including, for example, cap determination, distribution of allowances, auction design, and the reserve sale system, into a dynamic model that can be used by governments to create a program that is tailored to their requirements. Using Bayesian game theory, we also modeled different auction formats for a cap and trade program, including a single-stage design that has a deterministic reserve sale component and a two-stage game that requires firms to make bids for both the auction and the reserve sale. Running simulations of these auction games, we were able to evaluate how the addition of a price ceiling and single-turn purchasing limits impacts the behavior and costs of regulated firms. We found that the effect of a price ceiling on firms very much depends on relative demand for allowances. Single-turn reserve purchasing limits did not impact the aggregate cost for all firms, but greatly reduced the standard deviation of bid amounts. Finally, firms generally had a higher allowance acquisition cost in the two-stage auction model than in the one-stage model.