Distributed Nash Equilibrium Seeking in Consistency-Constrained Multicoalition Games

Zhou, Jialing; Lv, Yuezu; Wen, Guanghui; Lü, Jinhu; Zheng, Dezhi

doi:10.1109/tcyb.2022.3155687

Cited by 22 publications

(15 citation statements)

References 21 publications

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“…which follows from the inequality system of Equation (21). Combining the two inequalities results in α ≤ , choosing α ∈ (0, min{α * (α), α A , α σ }) results in ρ(A τ (α)) < 1.…”

Section: A Supporting Propositionmentioning

confidence: 96%

“…In [19], the results of [18] are generalized for directed communication architectures without the limitation to a leader-based information exchange between the clusters, which enables a faster convergence. Similar algorithms are proposed in [20] and [21] for unconstrained multi-cluster games with directed communication architectures. Thus, there already exist several versions of gradient-based algorithms for solving multi-cluster games in a distributed manner.…”

Section: Introductionmentioning

confidence: 99%

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Projected gradient-tracking in multi-cluster games and its application to power management

Zimmermann¹,

Tatarenko²,

Willert³

et al. 2022

Preprint

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We are concerned with a distributed approach to solve multi-cluster games arising in multi-agent systems. In such games, agents are separated into distinct clusters. The agents belonging to the same cluster cooperate with each other to achieve a common cluster goal while a non-cooperative game is played between the clusters. To be able to deal with the sparsity of information, as each agent only knows a specific part of the problem, we combine gradient-tracking and consensus methods for information distribution into an algorithm that can solve both the cooperative and non-cooperative problem in a single run. The constraints of the problem are taken into account by the corresponding projection operators and linear convergence is proven given an appropriate constant step size. The algorithm is applied to a day-ahead power management problem, posed as a multi-cluster game, and its efficiency is demonstrated by simulations.

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Section: A Supporting Propositionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Projected gradient-tracking in multi-cluster games and its application to power management

Zimmermann¹,

Tatarenko²,

Willert³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The proposed model can be viewed as a new type of multicoalition game, as it shares the core feature of capturing the cooperation of agents that belongs to the same coalition and the conflicts of interest among different coalitions. Existing studies on multi-coalition games can be found in [15]- [22] and the reference therein, which can be generally classified into two categories according to whether or not intra-coalition consistency constraints are involved. Specifically, the agent states in each coalition are free of coupled constraints in one category of studies [17]- [19], while in the other, are demand to reach an agreement [15], [16], [20]- [22].…”

Section: Introductionmentioning

confidence: 99%

“…Existing studies on multi-coalition games can be found in [15]- [22] and the reference therein, which can be generally classified into two categories according to whether or not intra-coalition consistency constraints are involved. Specifically, the agent states in each coalition are free of coupled constraints in one category of studies [17]- [19], while in the other, are demand to reach an agreement [15], [16], [20]- [22].…”

Section: Introductionmentioning

confidence: 99%

“…Along this line, directed and switching topologies are further considered in [18], and discrete-time gradient-free algorithm design for the case with unknown expressions of objective functions is studied in [19]. For multicoalition games with intra-coalition consistency constraints, a generalized nonsmooth distributed NE seeking algorithm is designed with continuous-time setting in [20]; while discretetime algorithms are developed under undirected and directed network topologies in [21] and [22] respectively. It is worth noting that, although multi-coalition games have been studied with several NE seeking algorithms developed, research on the proposed multi-coalition game with coupled equality constraint in the context of resource allocation has not been reported yet.…”

Section: Introductionmentioning

confidence: 99%

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Distributed Resource Allocation over Multiple Interacting Coalitions: A Game-Theoretic Approach

Wen¹,

Lv²,

Yang³

et al. 2022

Preprint

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Despite many distributed resource allocation (DRA) algorithms have been reported in literature, it is still unknown how to allocate the resource optimally over multiple interacting coalitions. One major challenge in solving such a problem is that, the relevance of the decision on resource allocation in a coalition to the benefit of others may lead to conflicts of interest among these coalitions. Under this context, a new type of multi-coalition game is formulated in this paper, termed as resource allocation game, where each coalition contains multiple agents that cooperate to maximize the coalition-level benefit while subject to the resource constraint described by a coupled equality. Inspired by techniques such as variable replacement, gradient tracking and leader-following consensus, two new kinds of DRA algorithms are developed respectively for the scenarios where the individual benefit of each agent explicitly depends on the states of itself and some agents in other coalitions, and on the states of all the game participants. It is shown that the proposed algorithms can converge linearly to the Nash equilibrium (NE) of the multicoalition game while satisfying the resource constraint during the whole NE-seeking process. Finally, the validity of the present allocation algorithms is verified by numerical simulations.

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Distributed event‐triggered generalized Nash equilibrium seeking in multi‐coalition noncooperative games with coupling constraints

Zhu

et al. 2023

Asian Journal of Control

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This paper is concerned with a multi‐coalition noncooperative game with coupling equality constraints. Each coalition is a player consisted of multiple agents in noncooperative games and desire to minimize its own objective function based on local information. Each agent as actual decision maker in the same coalition is to optimize the objective function of the coalition cooperately. To seek a generalized Nash equilibrium (GNE) of the multi‐coalition game, a distributed continuous‐time algorithm is developed. Moreover, to further reduce the communication among agents and coalitions, an event‐triggered mechanism (ETM) is introduced for the multi‐coalition game. By using ETM, a novel distributed GNE seeking algorithm is proposed, where agents and coalitions are allowed to exchange estimation information with neighbors only when the triggering condition is satisfied. Remarkably, the proposed event‐triggered scheme introduces internal variables to regulate its threshold dynamically, which excludes Zeno behavior. By Lyapunov analysis, it is proved that the coalitions' decision variables converge to a GNE in both algorithms. Finally, the effectiveness of the proposed methods is validated by numerical simulations.

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Distributed Nash Equilibrium Seeking in Consistency-Constrained Multicoalition Games

Cited by 22 publications

References 21 publications

Projected gradient-tracking in multi-cluster games and its application to power management

Projected gradient-tracking in multi-cluster games and its application to power management

Distributed Resource Allocation over Multiple Interacting Coalitions: A Game-Theoretic Approach

Distributed event‐triggered generalized Nash equilibrium seeking in multi‐coalition noncooperative games with coupling constraints

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