Game Theoretic Interaction and Decision: A Quantum Analysis

Ulrich Faigle () and Michel Grabisch

Games, 2017, vol. 8, issue 4, 1-25

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)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2073-4336/8/4/48/pdf (application/pdf)
https://www.mdpi.com/2073-4336/8/4/48/ (text/html)

Related works:
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)
Working Paper: Game Theoretic Interaction and Decision: A Quantum Analysis (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:8:y:2017:i:4:p:48-:d:117821

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().