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Quantum social game theory

Author

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  • Arfi, Badredine
Abstract
Most game-theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis. This paper explores the effects of non-independence on strategic interaction. Two types of non-independence effects are considered. First, the paper considers subjective non-independence at the level of the individual actor by looking at how choice ambivalence shapes the decision-making process. Specifically, how do alternative individual choices superpose with one another to “constructively/destructively” shape each other's role within an actor's decision-making process? This process is termed as quantum superposition of alternative choices. Second, the paper considers how inter-subjective non-independence across actors engenders collective strategies among two or more interacting actors. This is termed as quantum entanglement of strategies. Taking into account both types of non-independence effect makes possible the emergence of a new collective equilibrium, without assuming signaling, prior “contract” agreement or third-party moderation, or even “cheap talk”. I apply these ideas to analyze the equilibrium possibilities of a situation wherein N actors play a quantum social game of cooperation. I consider different configurations of large-N quantum entanglement using the approach of density operator. I specifically consider the following configurations: star-shaped, nearest-neighbors, and full entanglement.

Suggested Citation

  • Arfi, Badredine, 2007. "Quantum social game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 794-820.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:2:p:794-820
    DOI: 10.1016/j.physa.2006.06.027
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    References listed on IDEAS

    as
    1. Badredine Arfi, 2005. "Resolving the Trust Predicament: A Quantum Game-theoretic Approach," Theory and Decision, Springer, vol. 59(2), pages 127-174, September.
    2. Kydd, Andrew, 2000. "Trust, Reassurance, and Cooperation," International Organization, Cambridge University Press, vol. 54(2), pages 325-357, April.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Edward W. Piotrowski & Jan Sladkowski, "undated". "An Invitation to Quantum Game Theory," Departmental Working Papers 15, University of Bialtystok, Department of Theoretical Physics.
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    Cited by:

    1. Ali Hussein Samadi & Afshin Montakhab & Hussein Marzban & Sakine Owjimehr, 2017. "Quantum Barro--Gordon Game in Monetary Economics," Papers 1708.05689, arXiv.org.
    2. Samadi, Ali Hussein & Montakhab, Afshin & Marzban, Hussein & Owjimehr, Sakine, 2018. "Quantum Barro–Gordon game in monetary economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 94-101.

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