I found some references that might help you explore this topic. Other topics like game theory can also be applied to border carbon adjustments.
This is an excerpt from the website: "the author investigates complementing the EU ETS with a carbon price on traded goods, through so-called Border Carbon Adjustments (BCA), and finds this would most affect the poorest as well as the richest consumers in the EU. This is the first estimate of the EU-wide consumer incidence of BCA to complement the EU ETS." They have a working paper you can download.
Here is an excerpt from the abstract: "This paper
advances two arguments. First, it argues that the conventional view of Border Carbon Adjustments (BCAs) as a “dirty” trade barrier should be turned on its head. Rather, the absence of a carbon price comprises an implicit subsidy to dirtier production in non-regulated markets. Second, BCAs could act as a gamechanger when climate policy negotiations move at a glacial pace, if at all. Materially stronger progress could be achieved indirectly from the threat of unilateral trade policies. The paper shows how this could come about, using a simple political game theory model."
Vivid Economics: https://www.vivideconomics.com/casestudy/border-carbon-adjustments-and-industrial-competitiveness-in-a-european-green-deal/
Here is an excerpt from the website: "Driving industrial decarbonisation while safeguarding international competitiveness is a major policy challenge. As part of the European Green Deal, the EU is considering the introduction of a Border Carbon Adjustment (BCA) to ensure that the price of imports into the EU more accurately reflects the environmental costs of their carbon content. BCAs could be an alternative to free allocation to emissions-intensive trade-exposed sectors as a measure to address the risk of carbon leakage in the EU’s ETS." They have a report you can download too.