Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games

Burhaneddin İzgi, Murat Özkaya, Nazım Kemal Üre and Matjaž Perc

Applied Mathematics and Computation, 2024, vol. 473, issue C

Abstract: In this paper, we present four alternative solution methods to Shapley iteration for the solution of stochastic matrix games. We first combine the extended matrix norm method for stochastic matrix games with Shapley iteration and then state and prove the weak and strong hybrid versions of Shapley iterations. Then, we present the semi-extended matrix norm and iterative semi-extended matrix norm methods, which are analytic-solution-free methods, for finding the approximate solution of stochastic matrix games without determining the strategy sets. We illustrate comparisons between the Shapley iteration, weak and strong hybrid Shapley iterations, semi-extended matrix norm method, and iterative semi-extended matrix norm method with several examples. The results reveal that the strong and weak hybrid Shapley iterations improve the Shapley iteration and decrease the number of iterations, and the strong hybrid Shapley iteration outperforms all the other proposed methods. Finally, we compare these methods and present their performance analyses for large-scale stochastic matrix games as well.

Keywords: Game theory; Stochastic games; Matrix games; Shapley iteration; EMN method (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324001103
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:473:y:2024:i:c:s0096300324001103

DOI: 10.1016/j.amc.2024.128638

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().