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Games 2017, 8(4), 48; https://doi.org/10.3390/g8040048

Game Theoretic Interaction and Decision: A Quantum Analysis

1
Mathematisches Institut, Universität zu Köln, Weyertal 80, 50931 Köln, Germany
2
Paris School of Economics, University of Paris I, 106-112, Bd. de l’Hôpital, 75013 Paris, France
*
Author to whom correspondence should be addressed.
Received: 12 July 2017 / Revised: 19 October 2017 / Accepted: 21 October 2017 / Published: 6 November 2017
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Abstract

An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result, cooperation systems, decision systems and quantum systems all become visible as manifestations of special interaction systems. The treatment of the theory is purely mathematical and does not require any special knowledge of physics. It is shown how standard notions in cooperative game theory arise naturally in this context. In particular, states of general interaction systems are seen to arise as linear superpositions of pure quantum states and Fourier transformation to become meaningful. Moreover, quantum games fall into this framework. Finally, a theory of Markov evolution of interaction states is presented that generalizes classical homogeneous Markov chains to the present context. View Full-Text
Keywords: cooperative game; decision system; evolution; Fourier transform; interaction system; measurement; quantum game cooperative game; decision system; evolution; Fourier transform; interaction system; measurement; quantum game
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Faigle, U.; Grabisch, M. Game Theoretic Interaction and Decision: A Quantum Analysis. Games 2017, 8, 48.

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