Potential Games Design Using Local Information

Li, Changxi; He, Fenghua; Qi, Hongsheng; Cheng, Daizhan; Ma, Longbiao; Wu, Yonghong; Chen, Shuo

doi:10.1109/cdc.2018.8619561

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…By designing utility function, some systems can be translated into potential game, then using proper learning rule, the optimization can be finally achieved. The process can be explained in detail in [14] [15]. Rosenthal [26] described the situation of road congestion and proposed the network equilibrium model in [27].…”

mentioning

confidence: 99%

Traffic congestion pricing via network congestion game approach

Zhang¹,

Lu²,

Cao³

et al. 2021

Discrete &Amp; Continuous Dynamical Systems - S

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This paper investigates the optimization of traffic congestion systems via network congestion game approach. Firstly, using the semi-tensor product(STP) of matrices, the matrix expression of network congestion game is obtained. Secondly, a necessary and sufficient condition is proposed to guarantee that the traffic systems can be transformed into network congestion game with given performance criterion as its weighted potential function. Then an algorithm is provided to design the traffic congestion price in the case that conversion can be established. Thirdly, by designing proper learning rule, the optimization of traffic systems can be achieved when individuals optimize their own utility function. Moreover, two special cases which make our results more accord with reality and rich. Finally, an example is exploited to demonstrate the effectiveness of our obtained results.

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mentioning

confidence: 99%

Traffic congestion pricing via network congestion game approach

Zhang¹,

Lu²,

Cao³

et al. 2021

Discrete &Amp; Continuous Dynamical Systems - S

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Identification methods for ordinal potential differential games

Varga,

Huang,

Hohmann

2024

Comp. Appl. Math.

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This paper introduces two new identification methods for linear quadratic (LQ) ordinal potential differential games (OPDGs). Potential games are notable for their benefits, such as the computability and guaranteed existence of Nash Equilibria. While previous research has analyzed ordinal potential static games, their applicability to various engineering applications remains limited. Despite the earlier introduction of OPDGs, a systematic method for identifying a potential game for a given LQ differential game has not yet been developed. To address this gap, we propose two identification methods to provide the quadratic potential cost function for a given LQ differential game. Both methods are based on linear matrix inequalities (LMIs). The first method aims to minimize the condition number of the potential cost function’s parameters, offering a faster and more precise technique compared to earlier solutions. In addition, we present an evaluation of the feasibility of the structural requirements of the system. The second method, with a less rigid formulation, can identify LQ OPDGs in cases where the first method fails. These novel identification methods are verified through simulations, demonstrating their advantages and potential in designing and analyzing cooperative control systems.

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