Convergence in Human Decision-Making Dynamics

Ming Cao, Andrew Stewart and Naomi Ehrich Leonard

A class of binary decision-making tasks called the two-alternative forced-choice task has been used extensively in psychology and behavioral economics experiments to investigate human decision making. The human subject makes a choice between two options at regular time intervals and receives a reward after each choice; for a variety of reward structures, these experiments show convergence of the aggregate behavior to rewards that are often suboptimal. In this paper we present two models of human decision making: one is the Win-Stay, Lose-Switch (WSLS) model and the other is a deterministic limit of the popular Drift Diffusion (DD) model. With these models we prove convergence of the human behavior to the observed aggregate decision making for reward structures with matching points. The analysis is motivated by human-in-the-loop systems, where humans are often required to make repeated choices among finite alternatives in response to evolving system performance measures. We discuss application of the convergence result to design of human-in-the-loop systems using a map from the human subject to a human supervisor.