A holistic matrix norm-based alternative solution method for Markov reward games

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dc.authoridÖzkaya, Murat / 0000-0001-7241-4710
dc.contributor.authorİzgi, Burhaneddin
dc.contributor.authorÖzkaya, Murat
dc.contributor.authorÜre, Nazım Kemal
dc.contributor.authorPerc, Matjaz
dc.date.accessioned2025-01-27T20:24:30Z
dc.date.available2025-01-27T20:24:30Z
dc.date.issued2025
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractIn this study, we focus on examining single-agent stochastic games, especially Markov reward games represented in the form of a decision tree. We propose an alternative solution method based on the matrix norms for these games. In contrast to the existing methods such as value iteration, policy iteration, and dynamic programming, which are state-and-action-based approaches, the proposed matrix norm-based method considers the relevant stages and their actions as a whole and solves it holistically for each stage without computing the effects of each action on each state's reward individually. The new method involves a distinct transformation of the decision tree into a payoff matrix for each stage and the utilization of the matrix norm of the obtained payoff matrix. Additionally, the concept of the moving matrix is integrated into the proposed method to incorporate the impacts of all actions on the stage simultaneously, rendering the method holistic. Moreover, we present an explanatory algorithm for the implementation of the method and also provide a comprehensive solution diagram explaining the method figuratively. As a result, we offer a new and alternative perspective for solving the games with the help of the proposed method due to the simplicity of utilization of the matrix norms in addition to the existing methods. For clarification of the matrix norm-based method, we demonstrate the figurative application of the method on a benchmark Markov reward game with 2-stages and 2-actions and a comprehensive implementation of the method on a game consisting of 3-stages and 3-actions.
dc.description.sponsorshipScientific and Technological Research Council of Turkey (in Turkish: TUBIdot;TAK) [121E394]; Slovenian Research and Innovation Agency (Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije) [P1-0403, J1-2457, N1-0232]
dc.description.sponsorshipThis work is supported by the Scientific and Technological Research Council of Turkey (in Turkish: TUB & Idot;TAK) under grant agreement 121E394. M.P. was supported by the Slovenian Research and Innovation Agency (Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije) (Grant Nos. P1-0403, J1-2457, and N1-0232) . The authors would like to thank the anonymous referees and the editor for their valuable suggestions and comments that helped improve the article's content.
dc.identifier.doi10.1016/j.amc.2024.129124
dc.identifier.issn0096-3003
dc.identifier.issn1873-5649
dc.identifier.scopus2-s2.0-85206263483
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.amc.2024.129124
dc.identifier.urihttps://hdl.handle.net/20.500.12428/22253
dc.identifier.volume488
dc.identifier.wosWOS:001335739200001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Science Inc
dc.relation.ispartofApplied Mathematics and Computation
dc.relation.publicationcategoryinfo:eu-repo/semantics/openAccess
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20250125
dc.subjectGame theory
dc.subjectStochastic games
dc.subjectMarkov process
dc.subjectMarkov reward games
dc.subjectMatrix norm method
dc.titleA holistic matrix norm-based alternative solution method for Markov reward games
dc.typeArticle

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