A Passivity-Based Approach to Nash Equilibrium Seeking Over Networks

In this paper, we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information on the others' decisions. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2019-03, Vol.64 (3), p.1077-1092
Main Authors: Gadjov, Dian, Pavel, Lacra
Format: Article
Language:English
Subjects:
Convergence
Cost function
Distributed networks
Dynamics
Economic models
Game theory
Games
incremental passivity
Information exchange
Multiagent systems
Nash equilibrium
partial information
Passivity
Players
Synchronism
Vehicle dynamics
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Summary:In this paper, we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information on the others' decisions. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudogradient and assumes perfect information. We consider how to modify it in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players' actions. We derive the new dynamics based on the reformulation as a multiagent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors. Under a strict monotonicity property of the pseudogradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2833140