Quantum model of strategic decision-making based on the incompatibility of different views: new quantitative predictions and empirical results

This paper presents a new model of strategic decision-making based on the quantum probability theory as well as the experiment designed to test predictions of this model in the case of Prisoner's Dilemma game. We focused particularly on the level of cooperation and the discrepancy in willingness to cooperate among the different experimental treatments. Our research offers new conceptualization of the two-person game as well as quantitative predictions that were also tested in the laboratory experiment. The results of previous studies of Prisoner's Dilemma game (Shafir and Tversky, 1992; Pothos and Busemeyer, 2009) show that players largely prefer to defect if they know the strategy of their opponent but are much more willing to cooperate if the opponent's action is unknown. Such discrepancy means the violation of the sure thing principle, which is the fundamental principle of standard probability theory. As has been shown (e.g. Atmanspacher and Römer, 2012; Busemeyer and Lambert-Mogiliansky, 2009), the quantum probability theory - which is non-commutative and therefore able to predicate the interference and order effect - is more appropriate model for such behavior. There is a growing attention to the possibilities that the quantum probability theory offers to explain human cognition and decision comparing to the standard models. This theory employs the non-commutative algebra based on the Hilbert space representation of mental states, which can be seen as the generalization of the standard commutative model. We employed the results of the quantum theorizing, namely the model by Busemeyer and Bruza (2014), to derive new quantitative predictions for the strategic decision-making in the case of simple games. Our model shows that by using different views (self- and other-perspective), players employ mutually incompatible representations of the game, resulting in the interference effect. Due to this phenomena, we should expect the violation of the sure thing principle (in good accordance with the experimental findings of Shafir and Tversky) and consequently a higher level of cooperation in the one-shot Prisoner's Dilemma game. The quantum model of strategic decision-making offers alternative concept of rationality which predicts higher level of cooperation in Prisoner's Dilemma game as the direct consequence of the incompatibility of different views that players employ in the strategic decision-making. The experimental results are in good agreement with our prediction and confirm the appropriateness of the quantum model. Literature: Atmanspacher, H., Römer, H., 2012. Order effects in sequential measurements of non-commuting psychological observables. J. Math. Psychol. 56, 274–280. doi:10.1016/j.jmp.2012.06.003 Busemeyer, J.R., Bruza, P.D., 2014. Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge. Busemeyer, J.R., Lambert-Mogiliansky, A., 2009. An Exploration of Type Indeterminacy in Strategic Decision-Making, in: Bruza, P., Sofge, D., Lawless, W., Rijsbergen, K. van, Klusch, M. (Eds.), Quantum Interaction, Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 113–127. Pothos, E.M., Busemeyer, J.R., 2009. A quantum probability explanation for violations of “rational” decision theory. Proc. R. Soc. B Biol. Sci. 2171-2178. doi:10.1098/rspb.2009.0121 Shafir, E., Tversky, A., 1992. Thinking through uncertainty: Nonconsequential reasoning and choice. Cognit. Psychol. 24, 449–474. doi:10.1016/0010-0285(92)90015-T