Optimal taxation by two-agent reinforcement learning

Abstract: An economy’s tax policy is one of the vital moments for, on the one hand, stimulating economic growth and labor, and, on the other hand gaining revenues from economic performance. A sufficient level of tax revenues is further important to keep up with governmental obligations and social welfare. However, an increased tax rate may not always generate more tax revenues as it can demotivate the labor forces incentive to work, reduce the taxbase, and increase the unemployment rate which comes with harmful side effects. Finding an optimal tax rate or tax policy is a long-investigated field in economic theory, often referred to as the Laffer curve, and past research does not agree upon even the existence of an optimal tax rate or how to manage the associated labor-leisure trade-off. Nowadays, the development of artificial intelligence and its sub-field, multi-agent reinforcement learning (MARL), makes it possible to simulate real-world problems to investigate past theories. Past research suggests multi-agent reinforcement learning simulation to be a suitable method for investigating real-world problems and theoretical economic research. Even though its benefits in adoption and flexibility it is not widely practiced in tax policy making. This study examines the relationship between taxpayer and tax planner in a simplified two-agent economic simulation. Taxpayer agents can vary with their working rate to generate rewards from either salary or leisure, while the tax planner increases or decreases the tax rate for maximizing the tax revenues. Own generated-, random-, free-, national- and interval tax policies are practiced in the simulation to address the research questions. (1) How does taxpayer-agent behavior, in terms of labor, vary with different tax policies as well as a current national tax system through multi-agent reinforcement simulations? (2) Can MARL, through Q-learning, suggest a tax rate or tax policy that maximizes governmental revenues and agent utility? Here, Q- learning stands for quality learning, which is a subfield of multi-agent reinforcement learning that aims to estimate an agents expected reward taking an action for a given situation or state. The research clearly points at a decreasing working rate when tax rates increase and as a second consequence, decreases tax revenues. When the trade-off between labor and leisure is not evident in how to act, there is a higher uncertainty in the taxpayers’ decisions which supports usage of a reinforcement learning simulation as a suitable method. The simulations, in line with past research, suggest a progressive tax rate and further an optimal tax rate in the interval 30 - 40 %. In addition, the study supports Q-learning as a suitable method for economic simulations and opens the door for further for more complex real-world economic problems to be investigated by Q-learning.