Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback

Susu Jia; Zheng Kuang; Haihui Cheng; Xinzhu Meng; Tasawar Hayat; Aatef Hobiny

doi:10.1145/3544109.3544310

Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback

Susu Jia
, Zheng Kuang
, Haihui Cheng
, Xinzhu Meng
, Tasawar Hayat
, Aatef Hobiny

Shandong University of Science and Technology
King Abdulaziz University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

The classic Rock-Paper-Scissors (RPS) game has the only internal Nash Equilibrium (NE), which is not an Evolutionary Stable Strategy (ESS). Based on the replicator dynamics of evolutionary game theory, this paper considering the new RPS game that players have mutual feedback with environment, establishes a three-dimensional ordinary differential equation system. Through analysis and numerical simulations of this system, we prove the new RPS game has an ESS when the initial environment is not depleted and find three evolutionary internals including Evolutionary Equilibrium (EE) and periodic solutions.

Original language	English
Title of host publication	Proceedings of IPEC 2022 - 2022 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers
Publisher	Association for Computing Machinery
Pages	547-551
Number of pages	5
ISBN (Electronic)	9781450395786
DOIs	https://doi.org/10.1145/3544109.3544310
State	Published - 14 Apr 2022
Externally published	Yes
Event	3rd Asia-Pacific Conference on Image Processing, Electronics and Computers, IPEC 2022 - Dalian, China Duration: 14 Apr 2022 → 16 Apr 2022

Publication series

Name	ACM International Conference Proceeding Series

Conference

Conference	3rd Asia-Pacific Conference on Image Processing, Electronics and Computers, IPEC 2022
Country/Territory	China
City	Dalian
Period	14/04/22 → 16/04/22

Keywords

Rock-Paper-Scissors game
environmental feedback
evolutionary game theory
simulation

Access to Document

10.1145/3544109.3544310

Cite this

Jia, S., Kuang, Z., Cheng, H., Meng, X., Hayat, T., & Hobiny, A. (2022). Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback. In Proceedings of IPEC 2022 - 2022 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers (pp. 547-551). (ACM International Conference Proceeding Series). Association for Computing Machinery. https://doi.org/10.1145/3544109.3544310

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title = "Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback",

abstract = "The classic Rock-Paper-Scissors (RPS) game has the only internal Nash Equilibrium (NE), which is not an Evolutionary Stable Strategy (ESS). Based on the replicator dynamics of evolutionary game theory, this paper considering the new RPS game that players have mutual feedback with environment, establishes a three-dimensional ordinary differential equation system. Through analysis and numerical simulations of this system, we prove the new RPS game has an ESS when the initial environment is not depleted and find three evolutionary internals including Evolutionary Equilibrium (EE) and periodic solutions.",

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author = "Susu Jia and Zheng Kuang and Haihui Cheng and Xinzhu Meng and Tasawar Hayat and Aatef Hobiny",

note = "Publisher Copyright: {\textcopyright} 2022 ACM.; 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers, IPEC 2022 ; Conference date: 14-04-2022 Through 16-04-2022",

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doi = "10.1145/3544109.3544310",

language = "English",

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Jia, S, Kuang, Z, Cheng, H, Meng, X, Hayat, T & Hobiny, A 2022, Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback. in Proceedings of IPEC 2022 - 2022 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers. ACM International Conference Proceeding Series, Association for Computing Machinery, pp. 547-551, 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers, IPEC 2022, Dalian, China, 14/04/22. https://doi.org/10.1145/3544109.3544310

Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback. / Jia, Susu; Kuang, Zheng; Cheng, Haihui et al.
Proceedings of IPEC 2022 - 2022 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers. Association for Computing Machinery, 2022. p. 547-551 (ACM International Conference Proceeding Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Jia, Susu

AU - Kuang, Zheng

AU - Cheng, Haihui

AU - Meng, Xinzhu

AU - Hayat, Tasawar

AU - Hobiny, Aatef

PY - 2022/4/14

Y1 - 2022/4/14

N2 - The classic Rock-Paper-Scissors (RPS) game has the only internal Nash Equilibrium (NE), which is not an Evolutionary Stable Strategy (ESS). Based on the replicator dynamics of evolutionary game theory, this paper considering the new RPS game that players have mutual feedback with environment, establishes a three-dimensional ordinary differential equation system. Through analysis and numerical simulations of this system, we prove the new RPS game has an ESS when the initial environment is not depleted and find three evolutionary internals including Evolutionary Equilibrium (EE) and periodic solutions.

AB - The classic Rock-Paper-Scissors (RPS) game has the only internal Nash Equilibrium (NE), which is not an Evolutionary Stable Strategy (ESS). Based on the replicator dynamics of evolutionary game theory, this paper considering the new RPS game that players have mutual feedback with environment, establishes a three-dimensional ordinary differential equation system. Through analysis and numerical simulations of this system, we prove the new RPS game has an ESS when the initial environment is not depleted and find three evolutionary internals including Evolutionary Equilibrium (EE) and periodic solutions.

KW - Rock-Paper-Scissors game

KW - environmental feedback

KW - evolutionary game theory

KW - simulation

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DO - 10.1145/3544109.3544310

M3 - Conference contribution

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EP - 551

BT - Proceedings of IPEC 2022 - 2022 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers

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Jia S, Kuang Z, Cheng H, Meng X, Hayat T, Hobiny A. Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback. In Proceedings of IPEC 2022 - 2022 3rd Asia-Pacific Conference on Image Processing, Electronics and Computers. Association for Computing Machinery. 2022. p. 547-551. (ACM International Conference Proceeding Series). doi: 10.1145/3544109.3544310

Analysis and Simulations of the Rock-Paper-Scissors Game with Environmental Feedback

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