Algebras of Interaction and Cooperation

Ulrich Faigle, Alexander Schonhuth

Abstract


Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with ultiplicative structures, i.e., in algebras. Algebras, on the other hand, are conveniently viewed as polynomial algebras. In particular, basic nterpretations of natural numbers yield natural polynomial algebras and offer a new unifying view on cooperation and interaction. For example, the concept of Galois transforms and zero-dividends of cooperative games is introduced as a nonlinear analogue of the classical Harsanyi dividends. Moreover, the polynomial model unifies various versions of Fourier transforms. Tensor products of polynomial spaces establish a unifying model with quantum theory and allow to study classical cooperative games as interaction activities in a quantum-theoretic context.

Keywords


Ctivity System; Cooperative Game; Decision System; Evolution; Fourier Transform; Galois Transform; Interaction System; Measurement; Quantum Game.

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References


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DOI: http://dx.doi.org/10.30829/zero.v8i1.19947

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SLOT GACOR

SLOT GACOR

SLOT GACOR

SLOT GACOR

SLOT GACOR

SLOT GACOR

Department of Mathematics
Faculty of Science and Technology
Universitas Islam Negeri Sumatera Utara Medan 

Email: mtk.saintek@uinsu.ac.id

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