A quantum-like model for complementarity of preferences and beliefs in dilemma games

• Published in: Journal of mathematical psychology Vol. 78; pp. 96 - 106
• Main Authors: Denolf, Jacob, Martínez-Martínez, Ismael, Josephy, Haeike, Barque-Duran, Albert
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2017
• Subjects: Beliefs; Consensus effect; Positive-operator valued measure; Preferences; Sequential prisoner’s dilemma; Positive-operator valued measure; Preferences; Beliefs; Consensus effect; Sequential prisoner’s dilemma
• ISSN: 0022-2496; 1096-0880; 1096-0880
• DOI: 10.1016/j.jmp.2016.09.004

We propose a formal model to explain the mutual influence between observed behavior and subjects’ elicited beliefs in an experimental sequential prisoner’s dilemma. Three channels of interaction can be identified in the data set and we argue that two of these effects have a non-classical nature as shown, for example, by a violation of the sure thing principle. Our model explains the three effects by assuming preferences and beliefs in the game to be complementary. We employ non-orthogonal subspaces of beliefs in line with the literature on positive-operator valued measure. Statistical fit of the model reveals successful predictions. •We take a new look at data collected in a sequential prisoner’s dilemma.•We observe three behavioral effects and argue that two have a quantum-like nature.•Preferences and beliefs of the players exhibit complementarity.•We build a model in line with the theory of positive-operator valued measure.•The model is successfully applied to explain the experimental results.