Distributed consensus in noncooperative congestion games: An application to road pricing

In this study, the authors consider the large population dynamic games where each agent evolves according to a dynamic equation containing the input average of all agents. The long time average (LTA) cost that each agent aims to minimise is coupled with other agents' states via a population state average (PSA), which is also known as the mean field term. In order to design decentralised controls, the Nash certainty equivalence is introduced. It is shown that the resulting decentralised mean field control laws lead the system to mean-consensus asymptotically as time goes to infinity. The stability property of the mass behaviour and the almost sure asymptotic Nash equilibrium property of the optimal controls are also guaranteed, and the case with non-linear system dynamics is also discussed. In addition, the influence of inaccurate mean field information on individual agent is analysed. Finally, they investigate the socially cooperative formulation where the objective is to minimise the social cost as the sum of all individual LTA costs containing the PSA. In this case, they show that the decentralised mean field social controls are the same as the mean field Nash controls for infinite population systems.

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“…According to (4) and (5), each factory will receive a penalty because of the bias between x i andᾱp 0 , which is denoted by q(…”

Section: Motivational Examplementioning

confidence: 99%

Decentralised dynamic games for large population stochastic multi‐agent systems

Wang

Xiao

Xie

et al. 2015

IET Control Theory & Applications

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“…the interaction structure and learning algorithms can be designed separately [3], [4]. Some outstanding works include: (i) consensus/synchronization of multi-agent systems [3]; (ii) distributed optimization [5]; (iii) optimization in energy [6] and transportation networks [7], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

A strategic learning algorithm for state-based games

et al. 2020

Automatica

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Learning algorithm design for state-based games is investigated. A heuristic uncoupled learning algorithm, which is a two memory better reply with inertia dynamics, is proposed. Under certain reasonable conditions it is proved that for any initial state, if all agents in the state-based game follow the proposed learning algorithm, the action state pair converges almost surely to an action invariant set of recurrent state equilibria. The design relies on global and local searches with finite memory, inertia, and randomness. Finally, existence of time-efficient universal learning algorithm is studied. A class of state-based games is presented to show that there is no universal learning algorithm converging to a recurrent state equilibrium.

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“…Game-theoretical control has drawn considerable attention in recent years due to its widespread applications. Some representative works include: (i) consensus/synchronization of multi-agent systems [1]; (ii) distributed optimization [2], [3]; (iii) control in wireless networks; (iv) optimization in energy [4] and transportation networks [5], [6], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Potential Games Design Using Local Information

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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Consider a multiplayer game, and assume a system level objective function, which the system wants to optimize, is given. This paper aims at accomplishing this goal via potential game theory when players can only get part of other players' information. The technique is designing a set of local information based utility functions, which guarantee that the designed game is potential, with the system level objective function its potential function. First, the existence of local information based utility functions can be verified by checking whether the corresponding linear equations have a solution. Then an algorithm is proposed to calculate the local information based utility functions when the utility design equations have solutions. Finally, consensus problem of multiagent system is considered to demonstrate the effectiveness of the proposed design procedure.

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Distributed consensus in noncooperative congestion games: An application to road pricing

Cited by 46 publications

References 12 publications

Decentralised dynamic games for large population stochastic multi‐agent systems

Decentralised dynamic games for large population stochastic multi‐agent systems

A strategic learning algorithm for state-based games

Potential Games Design Using Local Information

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