Game Theoretic Interaction and Decision: A Quantum Analysis

Ulrich Faigle () and Michel Grabisch
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Ulrich Faigle: Mathematisches Institut, Universität zu Köln

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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.

Keywords: cooperative game; decision system; evolution; Fourier transform; interaction system; measurement; quantum game (search for similar items in EconPapers)
Date: 2017-11-06
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03220813v1
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Published in Games, 2017, 8 (4), pp.48. ⟨10.3390/g8040048⟩

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Related works:
Journal Article: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
Working Paper: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
Working Paper: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
Working Paper: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
Working Paper: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
Working Paper: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-03220813

DOI: 10.3390/g8040048

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