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., & Fallah, A. (2024). Homology groups and decomposition of the game complex. AUT Journal of Mathematics and Computing, (), -. doi: 10.22060/ajmc.2024.20822.1216
MLA
Neda Shojaee; Aidin Fallah. "Homology groups and decomposition of the game complex". AUT Journal of Mathematics and Computing, , , 2024, -. 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, (), pp. -. doi: 10.22060/ajmc.2024.20822.1216
VANCOUVER
Shojaee, N., Fallah, A. Homology groups and decomposition of the game complex. AUT Journal of Mathematics and Computing, 2024; (): -. doi: 10.22060/ajmc.2024.20822.1216
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