Nash and Wardrop Equilibria in Aggregative Games With Coupling Constraints

In this paper, we consider the problem of resource congestion control for competing online learning agents. On the basis of non-cooperative game as the model for the interaction between the agents, and the noisy online mirror ascent as the model for rational behaviour of the agents, we propose a novel pricing mechanism which gives the agents incentives for sustainable use of the resources. Our mechanism is distributed and resource-centric, in the sense that it is done by the resources themselves and not by a centralized instance, and that it is based rather on the congestion state of the resources than the preferences of the agents. In case that the noise is persistent, and for several choices of the intrinsic parameter of the agents, such as their learning rate, and of the mechanism parameters, such as the learning rate of -, the progressivity of the price-setters, and the extrinsic price sensitivity of the agents, we show that the accumulative violation of the resource constraints of the resulted iterates is sub-linear w.r.t. the time horizon. Moreover, we provide numerical simulations to support our theoretical findings.

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“…Setting (22) into (23) we obtain that SOL(X × R R ≥0 ,ṽ) coincides with the solution of KKT system: v(x) − ∇φ(x)λ = 0 0 ≤ λ ⊥ φ(x) ≤ 0 x ∈ X .…”

Section: F Kkt-system For Variational Inequalitymentioning

confidence: 99%

Robust Pricing Mechanism for Resource Sustainability Under Privacy Constraint in Competitive Online Learning Multi-Agent Systems

Tampubolon

Boche

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The following assumptions on the PG mapping are standard (e.g. [8,Th. 3], [10, Assumption 2], [24,Assumption 3]) and sufficient to ensure the convergence of standard GNE seeking algorithms.…”

Section: B Gne As Zeros Of a Monotone Operatormentioning

confidence: 99%

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

Belgioioso

Nedić

Grammatico

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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We design the first fully-distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the aggregate decision. The algorithm is derived by integrating dynamic tracking into a projected pseudo-gradient algorithm. The convergence analysis relies on the framework of monotone operator splitting and the Krasnosel'skii-Mann fixed-point iteration with errors.

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“…Further, this is the first paper that presents a general stochastic framework that simultaneously considers communication and activeness of the agents in NAGs in which the Gossip based communication protocol [23] can be encountered as a special case of the proposed framework. From other aspects, compared to aggregative games which consider the average strategy of whole population as a common coupling term among the agents [9]- [11], in this paper, the local aggregative term is studied in which only neighbors of each follower, as well as the leader, affect the follower's cost function. Compared to the literature of NAGs, those consider the local aggregative term, we have studied a general strongly convex cost function instead of quadratic one [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Leader–Follower Network Aggregative Game With Stochastic Agents’ Communication and Activeness

Shokri

Kebriaei

2020

IEEE Trans. Automat. Contr.

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This technical note presents a leader-follower scheme for network aggregative games. The followers and leader are selfish cost minimizing agents. The cost function of each follower is affected by strategy of leader and aggregated strategies of its neighbors through a communication graph. The leader infinitely often wakes up and receives the aggregated strategy of the followers, updates its decision value and broadcasts it to all the followers. Then, the followers apply the updated strategy of the leader into their cost functions. The establishment of information exchange between each neighboring pair of followers, and the activeness of each follower to update its decision at each iteration are both considered to be drawn from two arbitrary distributions. Moreover, a distributed algorithm based on subgradient method is proposed for updating the strategies of leader and followers. The convergence of the proposed algorithm to the unique generalized Nash equilibrium point of the game is proven in both almost sure and mean square senses.

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Nash and Wardrop Equilibria in Aggregative Games With Coupling Constraints

Cited by 113 publications

References 62 publications

Robust Pricing Mechanism for Resource Sustainability Under Privacy Constraint in Competitive Online Learning Multi-Agent Systems

Robust Pricing Mechanism for Resource Sustainability Under Privacy Constraint in Competitive Online Learning Multi-Agent Systems

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

Leader–Follower Network Aggregative Game With Stochastic Agents’ Communication and Activeness

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