A quantum model of strategic decision-making explains the disjunction effect in the Prisoner’s Dilemma game.

Abstract

The disjunction effect introduced in the famous study by Shafir and Tversky (1992) and confirmed in subsequent studies remains one of the key “anomalies” for the standard model of the Prisoner’s Dilemma game. In the last 10 years, a new approach has appeared that explains this effect using quantum probability theory. However, the existing results do not allow for a parameter-free test of these models. This article develops a simple quantum model of the Prisoner’s Dilemma game as well as a new experimental design that enables one to test the predictions of this model. The results show the viability of the quantum model and a substantial difference between women’s and men’s representations of the game.

Beliefs, Actions, and Rationality in Strategical Decisions

“…This new experiment included (a) a manipulation, such as Shafir and Tversky (1992), that did or did not provide the information about the other opponent's (e.g., Bill's) move before the player (e.g., Angela) made her decision; (b) a second manipulation, such as Croson (1999), that did or did not request a guess about the opponent (e.g., Bill) before the player (e.g., Angela) made her decision; and (c) a third manipulation that changed the order of guessing and decision. Tesar (2020) replicated both findings by Shafir and Tversky (1992) and Croson (1999), and also found that there was an order effect: The percentage of cooperation was 65% when the player (e.g., Angela) made a decision before guessing, but this percentage was significantly reduced to 42% when the player (e.g., Angela) guessed the opponent (Bill) first (pooled across guesses).…”

“…Tesar (2020) replicated and extended the work by Shafir and Tversky (1992) and Croson (1999). This new experiment included (a) a manipulation, such as Shafir and Tversky (1992), that did or did not provide the information about the other opponent's (e.g., Bill's) move before the player (e.g., Angela) made her decision; (b) a second manipulation, such as Croson (1999), that did or did not request a guess about the opponent (e.g., Bill) before the player (e.g., Angela) made her decision; and (c) a third manipulation that changed the order of guessing and decision.…”

“…On the one hand, quantum physicists, anticipating the development of quantum computers, have developed quantum strategies for games, which provide new and better equilibrium solutions (Alonso‐Sanz, 2019; Eisert, Wilkens, & Lewenstein, 1999; Meyer, 1999; Piotrowski & Sladkowski, 2002; Santos, 2020). On the other hand, quantum cognition researchers have used quantum theory to better describe how people actually make strategical decisions (Asano, Ohya, & Khrennikov, 2011; Denolf et al., 2016; Lambert‐Mogiliansky & Busemeyer, 2012; Martínez‐Martínez & Sánchez‐Burillo, 2016; Pothos & Busemeyer, 2009; Tesar, 2020; Yukalov & Sornette, 2014). In this article, (a) we review puzzling empirical findings using the PD game that motivates our consideration of a quantum approach to strategical decision making, (b) we describe a new experiment using a centipede game, and (c) we extend a quantum model, called the belief‐action entanglement (BAE) model, to account for the new empirical findings.…”

A Negation Quantum Decision Model to Predict the Interference Effect in Categorization

“…It can be used to explain many problems that are difficult to explain by traditional probability theories [14], especially the decision-making behavior with uncertainty [15]. The model explains come contradictions in human decision-making such as the separation effect, the interference effect of classification decision, the combination fallacy, the average effect, the unboxing effect, the order effect of reasoning, and the prisoner's dilemma [16,17,18,19,20]. At present, tons of decision models based on the quantum probability have been proposed, be it the quantum cognitive model [21], quantum-like models [22], generalized quantum models [23], and so on.…”

Primer on quantum cognition

“…But the order of measurement matters. In fact, it has been empirically found that the relative frequencies of pairs of answers to these questions change depending on order (Tesar, 2019).…”