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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