covering simplicial game complex
Combinatorics
2023-06-09 v1 Algebraic Topology
General Topology
Abstract
In this paper, we introduce a simplicial complex representation for finite non-cooperative games in the strategic form. The covering space of the simplicial game complex is introduced and we show that the covering complex is a powerful tool to find Nash Equilibrium simplices. This representation allows us to model the cost functions of a game as a weight number on a dual vertex of the strategy situation in some stars. It yields a canonical direct sum decomposition of an arbitrary game into three components, as the potential, harmonic and nonstrategic components.
Keywords
Cite
@article{arxiv.2306.05114,
title = {covering simplicial game complex},
author = {Neda Shojaee and Morteza M. Rezaii},
journal= {arXiv preprint arXiv:2306.05114},
year = {2023}
}
Comments
15 pages, 3 figures, 1 algorithm