期刊名称：Documents de Travail du Centre d'Economie de la Sorbonne
印刷版ISSN：1955-611X
出版年度：2017
出版社：Centre d'Economie de la Sorbonne
摘要：An interaction system has a finite set of agents that interact pairwise, dependingon the current state of the system. Symmetric decomposition of thematrix of interaction coefficients yields the representation of states by selfadjointmatrices and hence a spectral representation. As a result, cooperationsystems, decision systems and quantum systems all become visible asmanifestations of special interaction systems. The treatment of the theory ispurely mathematical and does not require any special knowledge of physics.It is shown how standard notions in cooperative game theory arise naturallyin this context. In particular, Fourier transformation of cooperative gamesbecomes meaningful. Moreover, quantum games fall into this framework.Finally, a theory of Markov evolution of interaction states is presented thatgeneralizes classical homogeneous Markov chains to the present context.
