Do Preferences and Beliefs in Dilemma Games Exhibit Complementarity?

Martínez-Martínez, Ismael; Denolf, Jacob; Barqué-Duran, Albert

doi:10.1007/978-3-319-28675-4_11

Cited by 2 publications

(3 citation statements)

References 33 publications

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“…This idea was first explored in Martínez-Martínez et al (2015). We present a quantum-like model for preferences and beliefs (QP&B) that replicates the experimental results from Blanco et al (2014) while providing a novel theoretical approach on cognitive dynamics in strategic interactions.…”

Section: Introductionmentioning

confidence: 93%

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

Denolf

Martínez-Martínez

Josephy

et al. 2017

Journal of Mathematical Psychology

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9We 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.

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Section: Introductionmentioning

confidence: 93%

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

Denolf

Martínez-Martínez

Josephy

et al. 2017

Journal of Mathematical Psychology

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“…A first example where these new types of projectors on non-orthogonal subspaces have already been constructed and successfully applied was presented in [10] and later expanded upon in [7] (including a successful statistical test against experimental data) . The incentive of constructing them in this paradigm, lay in the emergence of a problematic dimensionality when following the traditional quantum-like course.…”

Section: Qpandb Modelmentioning

confidence: 99%

“…In this paper we present an idea which also goes beyond orthodox quantumlike techniques. This new technique was originally formulated for a specific setting in [10] and further developed and tested in the recently submitted [7]. In these two papers, a model is constructed which deals with the relationship of a participant's beliefs and preferences in a game theoretic setting, taken from [3].…”

Section: Introductionmentioning

confidence: 99%

A First Attempt at Ordinal Projective Measurement

Denolf

2017

Quantum Interaction

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To our knowledge, all applications of the quantum framework in social sciences are used to model measurements done on a discrete nominal scale. However, especially in cognition, experiments often produce data on an ordinal scale, which implies some internal structure between the possible outcomes. Since there are no ordinal scales in physics, orthodox projection-valued measurement (PVM) lacks the tools and methods to deal with these ordinal scales. Here, we sketch out an attempt to incorporate the ordinal structure of outcomes into the subspaces representing these outcomes. This will also allow us to reduce the dimensionality of the resulting Hilbert spaces, as these often become too high in more complex quantum-like models. To do so, we loosen restrictions placed upon the PVM (and even POVM) framework. We discuss the two major consequences of this generalization: scaling and the loss of repeatability. We also present two applications of this approach, one in game theory and one concerning Likert scales.

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Do Preferences and Beliefs in Dilemma Games Exhibit Complementarity?

Cited by 2 publications

References 33 publications

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

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

A First Attempt at Ordinal Projective Measurement

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