A Nash-Type Fictitious Game Framework to Time-Inconsistent Stochastic Control Problems

Ni, Yuan‐Hua; Si, Binbin; Zhang, Xinzhen

doi:10.1137/19m1281885

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2023

2025

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Cited by 3 publications

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“…Game theory was pioneered by John von Neumann to study the behavior in economic society 1 . Then, it has been developed rapidly and applied widely in various communities, including biology 2,3 , economics 4 , and engineering 5,6 . The concept of potential games was first put forward by Rosenthal 7 , which is called "congestion games".…”

Section: Introductionmentioning

confidence: 99%

On Equivalence of State Based Potential Games

Wang

2023

Preprint

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By the method of semi-tensor product of matrices, state based potential games are investigated. Firstly, using the potential equation, a necessary and sufficient condition and a sufficient condition are proposed, respectively, to verify whether a state based game is potential. Then two static equivalence conditions of state based potential games are presented. Furthermore, the dynamic equivalence is given such that the state based games dynamically equivalent to the state based potential games have similar dynamic properties. Lastly, the concept of state based networked evolutionary games is proposed. A necessary and sufficient condition is given to assure a state based networked evolutionary game is potential.

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