Distributed generalized Nash equilibrium seeking in aggregative games under partial-decision information via dynamic tracking

Belgioioso, Giuseppe; Nedić, Angelia; Grammatico, Sergio

doi:10.1109/cdc40024.2019.9029883

Cited by 8 publications

(6 citation statements)

References 27 publications

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“…We conclude the section with the most general theoretical result of the paper, namely, the convergence of the closed-loop dynamics to a neighborhood of a v-GNE of the game in (6).…”

Section: Assumption 3 (Persistence Of Excitation)mentioning

confidence: 97%

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Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control

Krilašević¹,

Grammatico²

2020

Preprint

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In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose a novel continuous-time solution algorithm that uses regular projections and first-order information. As second main contribution, we design a data-driven variant of the former algorithm where each agent estimates their individual pseudogradient via zero-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control. Third, we generalize our setup and results for multi-agent systems with nonlinear dynamics. Finally, we apply our algorithms to connectivity control in robotic sensor networks and distributed wind farm optimization.

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“…We conclude the section with the most general theoretical result of the paper, namely, the convergence of the closed-loop dynamics to a neighborhood of a v-GNE of the game in (6).…”

Section: Assumption 3 (Persistence Of Excitation)mentioning

confidence: 97%

“…We assume that there exists a central coordinator who is capable of bidirectional communication on a star-shaped network with the agents, which is a frequent assumption in semi-decentralized algorithms [5], [6]. The central coordinator is tasked with computation of the dual variables.…”

Section: ]mentioning

confidence: 99%

Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control

Krilašević¹,

Grammatico²

2020

Preprint

Self Cite

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“…dual and auxiliary variables. The latter algorithmic setup is also called partialdecision information [20], [21], because the agents do not have direct access to the aggregative effect on their cost functions, thus they should estimate it via reliable, truthful peer-to-peer communications, e.g. via cooperative consensus protocols.…”

Section: A Aggregative Gamesmentioning

confidence: 99%

“…where ω k = col(x k , λ k ) and ωk = col(x k , λk ) are the stacked vectors of the iterates and R FB is the FB operator defined in (21). The convergence analysis of inertial schemes as in (23) are studied in [36]; while more precise conditions for the convergence of ( 23) are derived in [37, Th.…”

Section: Inertial Pfb Algorithmmentioning

confidence: 99%

Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games

Belgioioso,

Grammatico

2020

Preprint

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We address the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints. We focus on semi-decentralized communication architectures, where there is a central coordinator able to gather and broadcast signals of aggregative nature to the agents. By exploiting the framework of monotone operator theory and operator splitting, we first critically review the most relevant available algorithms and then design two novel schemes: (i) a single-layer, fixed-step algorithm with convergence guarantee for general (non-cocoercive, non-strictly) monotone aggregative games and (ii) a single-layer proximal-type algorithm for a class of monotone aggregative games with linearly coupled cost functions. We also design novel accelerated variants of two algorithms via (alternating) inertial steps. Finally, we show via numerical simulations that the proposed algorithms outperform those in the literature in terms of convergence speed.

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“…The computational methods of GNEs have been studied in [11], [12]. This paper falls in the category of constrained games with asymmetric constraint information, which have been investigated in [13], [14], [15], [16]. Most of the existing work focus on the algorithm design to find GNEs of this class of games, while this work aims to characterize the GNE and study the impact of the information structure on the GNEs.…”

Section: Introductionmentioning

confidence: 99%

Locally-Aware Constrained Games on Networks

Peng¹,

Liu

et al. 2021

2021 American Control Conference (ACC)

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Network games have been instrumental in understanding strategic behaviors over networks for applications such as critical infrastructure networks, social networks, and cyberphysical systems. One critical challenge of network games is that the behaviors of the players are constrained by the underlying physical laws or safety rules, and the players may not have complete knowledge of network-wide constraints. To this end, this paper proposes a game framework to study constrained games on networks, where the players are locally aware of the constraints. We use awareness levels to capture the scope of the network constraints that players are aware of. We first define and show the existence of generalized Nash equilibria (GNE) of the game, and point out that higher awareness levels of the players would lead to a larger set of GNE solutions. We use necessary and sufficient conditions to characterize the GNE, and propose the concept of the dual game to show that one can convert a locally-aware constrained game into a two-layer unconstrained game problem. We use linear quadratic games as case studies to corroborate the analytical results, and in particular, show the duality between Bertrand games and Cournot games.

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Distributed generalized Nash equilibrium seeking in aggregative games under partial-decision information via dynamic tracking

Cited by 8 publications

References 27 publications

Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control

Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control

Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games

Locally-Aware Constrained Games on Networks

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