Bistable Probabilities: A Unified Framework for Studying Rationality and Irrationality in Classical and Quantum Games

Abstract: This article presents a unified probabilistic framework that allows both rational and irrational decision making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of game theoretic models, which assumes that a decision maker chooses the best action according to their preferences. In this article, we define irrationality as a deviation from a rational choice. Bistable probabilities are proposed as a principled and straight forward means for modeling irrational decision making in games. Bistable variants of classical and quantum Prisoner's Dilemma, Stag Hunt and Chicken are analyzed in order to assess the effect of irrationality on agent utility and Nash equilibria. It was found that up to three Nash equilibria exist for all three classical bistable games and maximal utility was attained when agents were rational. Up to three Nash equilibria exist for all three quantum bistable games, however, utility was shown to increase according to higher levels of agent irrationality.