A decade after the publication of seminal papers on personal carbon trading (PCT), few empirical studies on its implementation exist. Investigating how to design, set up and implement a PCT scheme for a community or country raises several difficulties. For instance, it is unclear how to introduce a reduction rate of CO2 allowances to ensure a steady decrease in CO2 emissions from households. Computational approaches have been introduced to address these challenges of PCT by providing an opportunity to test counterfactual scenarios. Among the benefits of an agent-based modeling approach (ABM) is the potential to directly address dynamic developments and introduce counterfactual situations. In this paper, we review existing modeling approaches and present an ABM for PCT. With simulations of an artificial population of 1000 and 30,000 agents, we address questions on the price and reduction rate of allowances. A key contribution of our model is the inclusion of an adaptive reduction rate, which reduces the yearly allocated amount of allowances depending on a set CO2 abatement target. The results confirm that increased emissions targets are related to higher allowance prices and a higher proportion of buying households. Our analysis also suggests a significant path dependence in the dynamics of allowance prices and availability, but that adaptive reduction rates have little impact on outcomes other than the price. We discuss data availability and computational challenges to modeling a PCT scheme with an ABM. Ideal data to populate an ABM on PCT are not available due to the lack of real-world implementations of a PCT. Nonetheless, meaningful insights about the dynamics and the focal variables in a PCT scheme can be generated by the exploratory use of an ABM. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.