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arXiv · 2306.05114

covering simplicial game complex

Neda Shojaee·Morteza M. Rezaii
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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.

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Neda Shojaee, Morteza M. Rezaii. 2023-06-08. covering simplicial game complex. https://arxiv.org/abs/2306.05114

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