How Irrationality Shapes Nash Equilibria: A Prospect-Theoretic Perspective

Abstract: Noncooperative games with uncertain payoffs have been classically studied under the expected-utility theory framework, which relies on the strong assumption that agents behave rationally. However, simple experiments on human decision makers found them to be not fully rational, due to their subjective risk perception. Prospect theory was proposed as an empirically-grounded model to incorporate irrational behaviours into game-theoretic models. But, how prospect theory shapes the set of Nash equilibria when considering irrational agents, is still poorly understood. To this end, we study how prospect theoretic transformations may generate new equilibria while eliminating existing ones. Focusing on aggregative games, we show that capturing users' irrationality can preserve symmetric equilibria while causing the vanishing of asymmetric equilibria. Further, there exist value functions which map uncountable sets of equilibria in the expected-utility maximization framework to finite sets. This last result may shape some equilibrium selection theories for human-in-the-loop systems where computing a single equilibrium is insufficient and comparison of equilibria is needed.