On classification of the genetic and evolution rock-paper-scissor algebras

In recent decades in game theory, evolutionary and dynamically aspects have increased in popularity. An evolutionary zero-sum game generated by a Volterra quadratic stochastic operator V is called a Rock-Paper-Scissors (RPS) game if the operator V is a non-ergodic transformation. An algebra wi...

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Main Authors:	Ganikhodjaev, Nasir, Ftameh, Kalid
Format:	Conference or Workshop Item
Language:	English English
Published:	American Institute of Physics Inc. 2018
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/67472/ http://irep.iium.edu.my/67472/ http://irep.iium.edu.my/67472/ http://irep.iium.edu.my/67472/1/76920_On%20classification%20of%20the%20genetic_complete.pdf http://irep.iium.edu.my/67472/7/67472_On%20classification%20of%20the%20genetic%20and%20evolution_scopus.pdf

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spelling	iium-674722020-01-15T00:42:03Z http://irep.iium.edu.my/67472/ On classification of the genetic and evolution rock-paper-scissor algebras Ganikhodjaev, Nasir Ftameh, Kalid QA Mathematics In recent decades in game theory, evolutionary and dynamically aspects have increased in popularity. An evolutionary zero-sum game generated by a Volterra quadratic stochastic operator V is called a Rock-Paper-Scissors (RPS) game if the operator V is a non-ergodic transformation. An algebra with genetic realization (genetic algebra) is an algebra A over the real numbers R which has a finite basis and a multiplication table is generated by the Volterra quadratic stochastic operator. An evolution algebra over the real numbers R is an algebra with a basis on which multiplication is defined by the product of distinct basis terms being zero and the square of each basis element being a linear form in basis elements. We assume that the structure constants in the linear form are defined also by Volterra operator. We consider genetic and evolution algebras generated by non-ergodic Volterra operator. It is known that a zero-sum game generated by Volterra operator be a RPS game if and only if the operator is a non-ergodic transformation. We will call the genetic (evolution) algebra generated by non-ergodic Volterra operator RPS genetic (respectively RPS evolution) algebra. In this paper we investigate the problem of isomorphism of two RPS genetic (evolutionary) algebras and establish necessary and sufficient conditions when two such algebras will be isomorphic. American Institute of Physics Inc. 2018-07 Conference or Workshop Item NonPeerReviewed application/pdf en http://irep.iium.edu.my/67472/1/76920_On%20classification%20of%20the%20genetic_complete.pdf application/pdf en http://irep.iium.edu.my/67472/7/67472_On%20classification%20of%20the%20genetic%20and%20evolution_scopus.pdf Ganikhodjaev, Nasir and Ftameh, Kalid (2018) On classification of the genetic and evolution rock-paper-scissor algebras. In: International Conference on Mathematical Sciences and Technology 2018, 10th-12th Dec. 2018, Penang. https://aip.scitation.org/doi/abs/10.1063/1.5136358 10.1063/1.5136358
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics
spellingShingle	QA Mathematics Ganikhodjaev, Nasir Ftameh, Kalid On classification of the genetic and evolution rock-paper-scissor algebras
description	In recent decades in game theory, evolutionary and dynamically aspects have increased in popularity. An evolutionary zero-sum game generated by a Volterra quadratic stochastic operator V is called a Rock-Paper-Scissors (RPS) game if the operator V is a non-ergodic transformation. An algebra with genetic realization (genetic algebra) is an algebra A over the real numbers R which has a finite basis and a multiplication table is generated by the Volterra quadratic stochastic operator. An evolution algebra over the real numbers R is an algebra with a basis on which multiplication is defined by the product of distinct basis terms being zero and the square of each basis element being a linear form in basis elements. We assume that the structure constants in the linear form are defined also by Volterra operator. We consider genetic and evolution algebras generated by non-ergodic Volterra operator. It is known that a zero-sum game generated by Volterra operator be a RPS game if and only if the operator is a non-ergodic transformation. We will call the genetic (evolution) algebra generated by non-ergodic Volterra operator RPS genetic (respectively RPS evolution) algebra. In this paper we investigate the problem of isomorphism of two RPS genetic (evolutionary) algebras and establish necessary and sufficient conditions when two such algebras will be isomorphic.
format	Conference or Workshop Item
author	Ganikhodjaev, Nasir Ftameh, Kalid
author_facet	Ganikhodjaev, Nasir Ftameh, Kalid
author_sort	Ganikhodjaev, Nasir
title	On classification of the genetic and evolution rock-paper-scissor algebras
title_short	On classification of the genetic and evolution rock-paper-scissor algebras
title_full	On classification of the genetic and evolution rock-paper-scissor algebras
title_fullStr	On classification of the genetic and evolution rock-paper-scissor algebras
title_full_unstemmed	On classification of the genetic and evolution rock-paper-scissor algebras
title_sort	on classification of the genetic and evolution rock-paper-scissor algebras
publisher	American Institute of Physics Inc.
publishDate	2018
url	http://irep.iium.edu.my/67472/ http://irep.iium.edu.my/67472/ http://irep.iium.edu.my/67472/ http://irep.iium.edu.my/67472/1/76920_On%20classification%20of%20the%20genetic_complete.pdf http://irep.iium.edu.my/67472/7/67472_On%20classification%20of%20the%20genetic%20and%20evolution_scopus.pdf
first_indexed	2023-09-18T21:35:47Z
last_indexed	2023-09-18T21:35:47Z
_version_	1777412810577281024

On classification of the genetic and evolution rock-paper-scissor algebras

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