Do Preferences and Beliefs in Dilemma Games Exhibit Complementarity?

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9535)


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.


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


  1. Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Found. Sci. 1, 85–97 (1995)MathSciNetCrossRefGoogle Scholar
  2. Blanco, M., Engelmann, D., Koch, A.K., Normann, H.-T.: Preferences and beliefs in a sequential social dilemma: a within-subjects analysis. Games Econ. Behav. 87, 122–135 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Blanco, M., Engelmann, D., Normann, H.-T.: A within-subject analysis of other-regarding preferences. Games Econ. Behav. 72(2), 321–338 (2014)MathSciNetCrossRefGoogle Scholar
  4. Bohr, N.: On the notions of causality and complementarity. Science 111(2973), 51–54 (1950)CrossRefGoogle Scholar
  5. Bolle, F., Ockenfels, P.: Prisoner’s dilemma as a game with incomplete information. J. Econ. Psychol. 11(1), 69–84 (1990)CrossRefGoogle Scholar
  6. Bordley, R.F.: Quantum mechanical and human violations of compound probability principles: toward a generalized Heisenberg uncertainty principle. Oper. Res. 46, 923–926 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Brandenburger, A.: The relationship between quantum and classical correlation in games. Games Econ. Behav. 69(1), 175–183 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Brunner, N., Linden, N.: Connection between Bell nonlocality and Bayesian game theory. Nat. Commun. 4(2057), 1–6 (2013)Google Scholar
  9. Bruza, P., Busemeyer, J.R., Gabora, L.: Introduction to the special issue on quantum cognition. J. Math. Psychol. 53(5), 303–305 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Busemeyer, J.R., Bruza, P.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)CrossRefGoogle Scholar
  11. Busemeyer, J.R., Pothos, E.M.: Social projection and a quantum approach for behavior in Prisoner’s Dilemma. Psychol. Inq. 23(1), 28–34 (2012)CrossRefGoogle Scholar
  12. Busemeyer, J.R., Pothos, E.M., Franco, R., Trueblood, J.S.: A quantum theoretical explanation for probability judgment errors. Physchol. Rev. 118(2), 193–218 (2011)Google Scholar
  13. Busemeyer, J.R., Wang, Z., Townsend, J.T.: Quantum dynamics of human decision-making. J. Math. Psychol. 50, 220–241 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  14. Clark, K., Sefton, M.: The sequential prisoner’s dilemma: evidence on reciprocation. Econ. J. 11(468), 51–68 (2001)CrossRefGoogle Scholar
  15. Danilov, V.I., Lambert-Mogiliansky, A.: Measurable systems and social sciences. Math. Soc. Sci. 55, 315–340 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. Danilov, V.I., Lambert-Mogiliansky, A.: Expected utility theory under non-classical uncertainty. Theor. Decis. 68(1–2), 25–47 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. Denolf, J.: Subadditivity of episodic memory states: a complementarity approach. In: Atmanspacher, H., Bergomi, C., Filk, T., Kitto, K. (eds.) QI 2014. LNCS, vol. 8951, pp. 67–77. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  18. Deutsch, D.: Quantum theory of probability and decisions. Proc. Roy. Soc.A 455(1988), 3129–3137 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  19. Gabora, L., Aerts, D.: Contextualizing concepts using a mathematical generalization of the quantum formalism. J. Exper. Theor. Artif. Intell. 14(4), 327–358 (2002)CrossRefzbMATHGoogle Scholar
  20. beim Graben, P., Atmanspacher, H.: Extending the philosophical significance of the idea of complementarity. In: Atmanspacher, H., Primas, H. (eds.) Recasting Reality-Wolfgang Pauli’s Philosophical Ideas and Contemporary Science, pp. 99–113. Springer-Verlag, Heidelberg (2009)Google Scholar
  21. Hameroff, S.R.: The brain is both neurocomputer and quantum computer. Cogn. Sci. 31, 1035–1045 (2007)CrossRefGoogle Scholar
  22. Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, Cambridge (2012)Google Scholar
  23. Khrennikov, A.: Ubiquitous Quantum Structure: From Psychology to Finance. Springer, Berlin (2010)CrossRefGoogle Scholar
  24. La Mura, P.: Correlated equilibria of classical strategic games with quantum signals. Int. J. Quan. Inf. 3(1), 183–188 (2005)CrossRefzbMATHGoogle Scholar
  25. Lambert-Mogiliansky, A., Zamir, S., Zwirn, H.: Type indeterminacy: a model for the KT(Kahneman-Tversky)-man. J. Math. Psychol. 53, 349–361 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  26. Lambert-Mogiliansky, A., Martínez-Martínez, I.: Games with type indeterminate players: a Hilbert space approach to uncertainty and strategic manipulation of preferences. In: Proceedings of the Quantum Interaction Conference (2014, in press)Google Scholar
  27. Lichtenstein, S., Slovic, P.: The Construction of Preference. Cambridge University Press, Cambridge (2006)CrossRefGoogle Scholar
  28. Litt, A., Eliasmith, C., Kroon, F.W., Weinstein, S., Thagard, P.: Is the brain a quantum computer? Cogn. Sci. 30, 593–603 (2006)CrossRefGoogle Scholar
  29. Pothos, E.M., Busemeyer, J.R.: A quantum probability explanation for violations of ‘rational’ decision theory. Proc. Roy. Soc. B 276, 2171–2178 (2009)CrossRefGoogle Scholar
  30. Pothos, E.M., Busemeyer, J.R.: Can quantum probability provide a new direction for cognitive modeling? Behav. Brain Sci. 36, 255–327 (2013)CrossRefGoogle Scholar
  31. Pothos, E.M., Perry, G., Corr, P.J., Matthew, M.R., Busemeyer, J.R.: Understanding cooperation in the Prisoners Dilemma game. Pers. Individ. Differ. 51(3), 210–215 (2011)CrossRefGoogle Scholar
  32. Trueblood, J.S., Busemeyer, J.R.: A quantum probability account of order effects in inference. Cogn. Sci. 35, 1518–1552 (2011)CrossRefGoogle Scholar
  33. Wang, Z., Solloway, T., Shiffrin, R.M., Busemeyer, J.R.: Context effects produced by question orders reveal quantum nature of human judgments. Proc. Natl. Acad. Sci. USA 111(26), 9431–9436 (2014)CrossRefGoogle Scholar
  34. White, L.C., Pothos, E.M., Busemeyer, J.R.: Sometimes it does hurt to ask: the constructive role of articulating impressions. Cognition 133(1), 48–64 (2014)CrossRefGoogle Scholar
  35. Yearsley, J.M., Pothos, E.M.: Challenging the classical notion of time in cognition: a quantum perspective. Proc. Roy. Soc. B 281, 20133056 (2014)CrossRefGoogle Scholar
  36. Yearsley, J.M., Pothos, E.M., Hampton, J.A., Barque Duran, A.: Towards a quantum probability theory of similarity judgments. In: Proceedings of the Quantum Interaction Conference (2014, in press)Google Scholar
  37. Yukalov, V.I., Sornette, D.: Decision theory with prospect interference and entanglement. Theor. Decis. 70, 283–328 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Düsseldorf Institute for Competition Economics (DICE)Heinrich Heine Universität DüsseldorfDüsseldorfGermany
  2. 2.Department of Data AnalysisGhent UniversityGhentBelgium
  3. 3.Department of PsychologyCity University LondonLondonUK

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