TY - GEN
T1 - A Lagrangian approach to constrained potential games
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
AU - Zhu, Quanyan
PY - 2008
Y1 - 2008
N2 - In this paper, we use a Lagrangian approach to solve for Nash equilibrium in a continuous non-cooperative game with coupled constraints. We discuss the necessary and the sufficient conditions to characterize the equilibrium of the constrained games. In addition, we discuss the existence and uniqueness of the equilibrium. We focus on the class of potential games and point out a relation between potential games and centralized optimization. Based on these results, we illustrate the Lagrangian approach with symmetric quadratic games and briefly discuss the notion of game duality. In addition, we discuss two engineering potential game examples from network rate control and wireless power control, for which the Lagrangian approach simplifies the solution process.
AB - In this paper, we use a Lagrangian approach to solve for Nash equilibrium in a continuous non-cooperative game with coupled constraints. We discuss the necessary and the sufficient conditions to characterize the equilibrium of the constrained games. In addition, we discuss the existence and uniqueness of the equilibrium. We focus on the class of potential games and point out a relation between potential games and centralized optimization. Based on these results, we illustrate the Lagrangian approach with symmetric quadratic games and briefly discuss the notion of game duality. In addition, we discuss two engineering potential game examples from network rate control and wireless power control, for which the Lagrangian approach simplifies the solution process.
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U2 - 10.1109/CDC.2008.4738596
DO - 10.1109/CDC.2008.4738596
M3 - Conference contribution
AN - SCOPUS:62949133421
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2420
EP - 2425
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 9 December 2008 through 11 December 2008
ER -