To increase competition, control price, and decrease inefficiency in the carbon allowance auction market, limitations on bidding price and volume can be set.With limitations, participants have the same cap bidding price and volume. While without the limitations, participants have different values per unit of carbon allowance; therefore, some participants may be strong and the other week. Due to the impact of these limitations on the auction, this paper tries to compare the uniform and discriminatory pricing in a carbon allowance auction with and without the limitations utilizing a multi-agent-based model consisting of the government and supply chains. The government determines the supply chains’ initial allowances. The supply chains compete in the carbon auction market and determine their bidding strategies based on the Q-learning algorithm. Then they optimize their tactical and operational decisions. They can also trade their carbon allowances in a carbon trading market in which price is free determined according to carbon supply and demand. Results show that without the limitations, the carbon price in the uniform pricing is less than or equal to the discriminatory pricing method. At the same time, there are no differences between them in the case with limitations. Overall, the auction reduces the profit of the supply chains. This negative effect is less in uniform than discriminatory pricing in the case without the limitations. Nevertheless, the strong supply chains make huge profits from the auction when mitigation rate is high.

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