From weighted potential game to weighted harmonic game

It was shown that the vector space of finite non-cooperative games can be decomposed into three orthogonal subspaces: the pure potential games (PGs) (P), non-strategic games (N), and pure harmonic games (ℋ). This study proposes the concept of weighted harmonic game, and shows that in the aforementioned decomposition the P can be replaced by weighted pure PGs P w , and the ℋ can be replaced by WPHGs ℋ w . Then the bases for corresponding orthogonal subspaces are presented, respectively. Finally, certain properties of the new decomposed subspaces are investigated.

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

[2]  J. Nash.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[3]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

[4]  H. Singh,et al.  Introduction to game theory and its application in electric power markets , 1999 .

[5]  Jason R. Marden,et al.  Designing Games for Distributed Optimization , 2013, IEEE J. Sel. Top. Signal Process..

[6]  Nan Xiao,et al.  Distributed consensus in noncooperative congestion games: An application to road pricing , 2013, 2013 10th IEEE International Conference on Control and Automation (ICCA).

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

[8]  Daizhan Cheng,et al.  Dual expressions of decomposed subspaces of finite games , 2015, 2015 34th Chinese Control Conference (CCC).

[9]  Tiina Heikkinen,et al.  A potential game approach to distributed power control and scheduling , 2006, Comput. Networks.

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

[11]  Stef Tijs,et al.  CONGESTION MODELS AND WEIGHTED BAYESIAN POTENTIAL GAMES , 1997 .

[12]  Magnus Egerstedt,et al.  A Game Theoretic Approach to Distributed Coverage of Graphs by Heterogeneous Mobile Agents , 2013 .

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

[14]  Asuman E. Ozdaglar,et al.  Dynamics in near-potential games , 2011, Games Econ. Behav..

[15]  Jason R. Marden,et al.  Cooperative Control and Potential Games , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Jason R. Marden.  State based potential games , 2012, Autom..

[17]  Sonia Martínez,et al.  Distributed Coverage Games for Energy-Aware Mobile Sensor Networks , 2013, SIAM J. Control. Optim..

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

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

[20]  Xinyun Liu,et al.  On potential equations of finite games , 2015, Autom..