Carbon constrained electricity markets are a reality in 10 northeastern states and California in the US, as well as the European Union. Close to a Billion US Dollars have been spent by entities (mainly generators) in the Regional Greenhouse Gas Initiative in procuring CO2 allowances to meet binding emissions restrictions. In the near future, there are expected to be significant impacts due to the cap-and-trade program, especially when the cap stringency increases. In this research we develop a bilevel, complete-information, matrix game-theoretic model to assess the economic impact and make operational decisions in carbon-constrained restructured electricity markets. Our model is solved using a reinforcement learning approach, which takes into account the learning and adaptive nature of market participants. Our model also accounts for all the power systems constraints via a DC-OPF problem. We demonstrate the working of the model and compute various economic impact indicators such as supply shares, cost pass-through, social welfare, profits, allowance prices, and electricity prices. Results from a 9-bus power network are presented. (C) 2011 Elsevier Ltd. All rights reserved.