Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/179158 
Year of Publication: 
2017
Citation: 
[Journal:] Games [ISSN:] 2073-4336 [Volume:] 8 [Issue:] 4 [Publisher:] MDPI [Place:] Basel [Year:] 2017 [Pages:] 1-25
Publisher: 
MDPI, Basel
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.
Subjects: 
cooperative game
decision system
evolution
Fourier transform
interaction system
measurement
quantum game
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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