Complete Lattice Using Lexicographical Order and Its Application in Non-Cooperative Ordered Game
Abstract
One application of lattices in optimization is defining the equilibrium set of ordered games, typically using the usual (coordinate-wise) order, which is incomplete in Rn. This incompleteness makes some strategies incomparable, requiring a special game concept. Using a complete order, like the lexicographic order, results in a complete lattice. This study explores the properties of a complete lattice with lexicographic order for noncooperative games and provides a Python algorithm to determine the Nash equilibrium of a supermodular game.
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J. Bilbao, Cooperative games on combinatorial structures. Springer Science+Business Media, 2012, vol. 26.
M. Van der Merwe, Non-cooperative games on networks. Ph.D dissertation, Stellenbosch University, 2012.
F. R. Csori, Structural and computational aspects of simple and influence games. Tesis, Universitat Politecnica de Catalunya, 2014.
D. M. Topkis, “Minimizing a submodular function on a lattice,” Operations Research, vol. 26(2), pp. 305–321, 1978.
P. Milgrom and C. Shannon, “Monotone comparative statics,” Econometrica, vol. 62(1), pp. 157–180, 1994.
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G. Rota-Graziosi, “The supermodularity of the tax competition game,” J.Math.Econ., vol. 83, pp. 25–35, 2019.
G. Koshevoy, T. Suzuki, and D. Talman, “Supermodular ntu-games,” Oper. Res. Lett., vol. 44, pp. 446–450, 2016. doi: 10.1016/j.orl.2016.04.007
Published
2025-07-31
How to Cite
SETIAWAN, Rubono; KURDHI, Nughthoh Arfawi.
Complete Lattice Using Lexicographical Order and Its Application in Non-Cooperative Ordered Game.
Yugoslav Journal of Operations Research, [S.l.], july 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1361>. Date accessed: 31 aug. 2025.
doi: https://doi.org/10.2298/YJOR240815030S.
Issue
Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
