A reduction of greenhouse gas emissions has become one of the most important issues that power companies have to solve. The objective of this study is to assess performance of two kinds of environmental policies that are carbon tax and cap-and- trading of CO
2 emission permits on an electricity market. For that purpose, we develop a multi-agent model based on reinforcement learning that simulates a CO
2 emission trading market as well as an electricity market. By conducting model simulations, we obtain the following results. We confirm the major outputs of the model such as market shares and market prices of electricity in various carbon taxes. We also confirm duality principle between carbon tax and CO
2 emission cap-and- trading when the carbon price is at 2000 JPY/t-CO
2. However, in a case of different allocation of CO
2 emissions, we observe duality principle could collapse and the carbon price in the collapse case could become much higher than the carbon price with the duality principle. This is because the CO
2 allocation affects the income and expenditure of each agent and changes the strategy of each agent in the CO
2 market as well as the electricity market. Thus, the institutional design of CO
2 emission cap-and-trading requires careful consideration for income and expenditure of agents in the market.
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