Mathematical Game Theory: A New Approach
Abstract
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in particular, combinatorial and zero-sum games as well as models for investing and betting. n-person games are studied with emphasis on notions of utilities, potentials and equilibria, which allows to subsume cooperative games as special cases. The represenation of a game theoretic system in a Hilbert space furthermore establishes a link to the mathematical model of quantum mechancis and general interaction systems. The notes sketch an outline of the theory. Details are available as a textbook elsewhere.
Keywords
Cite
@article{arxiv.2012.01850,
title = {Mathematical Game Theory: A New Approach},
author = {Ulrich Faigle},
journal= {arXiv preprint arXiv:2012.01850},
year = {2023}
}