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Do Preferences and Beliefs in Dilemma Games Exhibit Complementarity?

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9535)

Abstract

Blanco et al. (2014) show in a novel experiment the presence of intrinsic interactions between the preferences and the beliefs of participants in social dilemma games. They discuss the identification of three effects, and we claim that two of them are inherently of non-classical nature. Here, we discuss qualitatively how a model based on complementarity between preferences and beliefs in a Hilbert space can give an structural explanation to two of the three effects the authors observe, and the third one can be incorporated into the model as a classical correlation between the observations in two subspaces. Quantitative formalization of the model and proper fit to the experimental observation will be done in the near future, as we have been given recent access to the original dataset.

Keywords

  • Quantum-like preferences and beliefs
  • Consensus effect
  • Social projection
  • Complementarity
  • Sequential prisoner’s dilemma

We would like to express our gratitude to the authors Mariana Blanco, Dirk Engelmann, Alexander K. Koch, and especially Hans-Theo Normann for providing access to their experimental dataset.

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Notes

  1. 1.

    Journal of Mathematical Psychology, 2009, volume 53, issue 5, and Topics in Cognitive Science, 2013, volume 5, issue 4.

  2. 2.

    Contributions to the Quantum Interaction conferences 2007–2014 held at Stanford, Oxford, DFKI Saarbrücken, AAAI Washington DC, RGU Aberdeen, Paris School of Economics, Leicester, and Filtzbach are available in the series Lecture Notes in Computer Science by Springer.

  3. 3.

    For the small game analyzed in this paper, it is enough for the reader to understand a player’s belief as the subjective distribution with which the agent judges the likelihood of realization of each possible state of the world that the player could face, and which in general, influences the type of payoffs to be received from the actions. Also, as an idealized object, we can consider the preferences as an individual’s attitude towards a set of outcomes, typically reflected through the actions taken in an explicit decision-making process. For more details, see Lichtenstein and Slovic (2006).

  4. 4.

    Please note that this is a preliminary proposal and the model may change substantially after proper fitting to the data set.

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Correspondence to Jacob Denolf .

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Martínez-Martínez, I., Denolf, J., Barque-Duran, A. (2016). Do Preferences and Beliefs in Dilemma Games Exhibit Complementarity?. In: Atmanspacher, H., Filk, T., Pothos, E. (eds) Quantum Interaction. QI 2015. Lecture Notes in Computer Science(), vol 9535. Springer, Cham. https://doi.org/10.1007/978-3-319-28675-4_11

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