Quasi-Potential Game

A new kind of finite games, called quasi-potential game (QPG), including ordinal QPG, weighted QPG, and exact QPG, is proposed. It is proved that though a QPG may not be a potential game, it has the properties of potential games. The necessary and sufficient condition for verifying QPG is obtained. The algorithm that makes the QPG converge to the Nash equilibrium is presented.

[1]  T. Shen,et al.  A logical network approximation to optimal control on a continuous domain and its application to HEV control , 2022, Science China Information Sciences.

[2]  Daizhan Cheng,et al.  A Comprehensive Survey on STP Approach to Finite Games , 2021, Journal of Systems Science and Complexity.

[3]  Daizhan Cheng,et al.  Weighted and Near Weighted Potential Games with Application to Game Theoretic Control , 2021, Autom..

[4]  Marceau Coupechoux,et al.  Distributed Learning in Noisy-Potential Games for Resource Allocation in D2D Networks , 2020, IEEE Transactions on Mobile Computing.

[5]  Lakhdar Sais,et al.  Solving a Potential Clustering Game , 2019, Int. J. Artif. Intell. Tools.

[6]  Shengwei Mei,et al.  Distributed Real-Time Economic Dispatch in Smart Grids: A State-Based Potential Game Approach , 2018, IEEE Transactions on Smart Grid.

[7]  D. Cheng,et al.  Vector space structure of finite evolutionary games and its application to strategy profile convergence , 2016, J. Syst. Sci. Complex..

[8]  Daizhan Cheng,et al.  On Decomposed Subspaces of Finite Games , 2016, IEEE Transactions on Automatic Control.

[9]  Daizhan Cheng,et al.  Modeling, Analysis and Control of Networked Evolutionary Games , 2015, IEEE Transactions on Automatic Control.

[10]  Daizhan Cheng,et al.  On finite potential games , 2014, Autom..

[11]  D. Cheng,et al.  An Introduction to Semi-Tensor Product of Matrices and Its Applications , 2012 .

[12]  Yusuke Hino,et al.  An improved algorithm for detecting potential games , 2011, Int. J. Game Theory.

[13]  Asuman E. Ozdaglar,et al.  A projection framework for near-potential games , 2010, 49th IEEE Conference on Decision and Control (CDC).

[14]  Asuman E. Ozdaglar,et al.  Dynamics in near-potential games , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[15]  Asuman E. Ozdaglar,et al.  Flows and Decompositions of Games: Harmonic and Potential Games , 2010, Math. Oper. Res..

[16]  Josef Hofbauer,et al.  A differential Game Approach to Evolutionary Equilibrium Selection , 2002, IGTR.

[17]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[18]  L. Shapley,et al.  Potential Games , 1994 .