In this paper, we introduce a novel simplicial complex named Game Complex for finite non-cooperative games in the strategic form. We prove that the number of Nash equilibrium in non-cooperative games with more than two players is the rank of the first homology group of the game complex. Furthermore, we give a decomposition of the game complex.
Shojaee,N. and Fallah,A. (2024). Homology groups and decomposition of the game complex. (e5506). AUT Journal of Mathematics and Computing, (), e5506 doi: 10.22060/ajmc.2024.20822.1216
MLA
Shojaee,N. , and Fallah,A. . "Homology groups and decomposition of the game complex" .e5506 , AUT Journal of Mathematics and Computing, , , 2024, e5506. doi: 10.22060/ajmc.2024.20822.1216
HARVARD
Shojaee N., Fallah A. (2024). 'Homology groups and decomposition of the game complex', AUT Journal of Mathematics and Computing, (), e5506. doi: 10.22060/ajmc.2024.20822.1216
CHICAGO
N. Shojaee and A. Fallah, "Homology groups and decomposition of the game complex," AUT Journal of Mathematics and Computing, (2024): e5506, doi: 10.22060/ajmc.2024.20822.1216
VANCOUVER
Shojaee N., Fallah A. Homology groups and decomposition of the game complex. AUT J Math Comput, 2024; (): e5506. doi: 10.22060/ajmc.2024.20822.1216
