On finite potential games
Automatica (Journal of IFAC)(2014)
摘要
linear system, called the potential equation (PE), is presented. It is proved that a finite game is potential if and only if its potential equation has solution. Some properties of the potential equation are obtained. Based on these properties, a closed form solution of the PE is obtained. Moreover, a formula based on the solution of the PE is obtained to calculate the potential function. Finally, it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential. Some interesting examples are presented to illustrate the theoretical results.
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关键词
Potential game,Potential equation,Networked evolutionary game,Semi-tensor product of matrices
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