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Distributed Nash Equilibrium Seeking by A Consensus Based Approach [article]

Maojiao Ye, Guoqiang Hu
2017 arXiv   pre-print
By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the non-cooperative games.  ...  In this paper, Nash equilibrium seeking among a network of players is considered.  ...  Distributed Nash Equilibrium Seeking by A Consensus Based Approach Maojiao Ye and Guoqiang Hu Abstract-In this paper, Nash equilibrium seeking among a network of players is considered.  ... 
arXiv:1602.00771v3 fatcat:zr27dyseure3tbjm6yhylkda2y

Nash Equilibrium Seeking for General Linear Systems with Disturbance Rejection [article]

Xin Cai, Feng Xiao, Bo Wei, Mei Yu, Fang Fang
2021 arXiv   pre-print
This paper explores aggregative games in a network of general linear systems subject to external disturbances.  ...  all players to evolve to Nash equilibrium regardless the effect of disturbances.  ...  The purpose of distributed Nash equilibrium seeking is to design the strategy-updating rule for players to reach the NE of the game, at which each agent has the minimum cost.  ... 
arXiv:2110.08844v2 fatcat:3cuuy7oqorddvnchh6suyyq66u

Projected-gradient algorithms for generalized equilibrium seeking in Aggregative Games are preconditioned Forward-Backward methods [article]

Giuseppe Belgioioso, Sergio Grammatico
2018 arXiv   pre-print
via operator splitting methods" for generalized Nash equilibrium seeking in aggregative games.  ...  More generally, we provide a unifying operator-theoretic ground to design projected-gradient methods for generalized equilibrium seeking in aggregative games.  ...  A popular class of algorithms for Nash equilibrium seeking is that of projected-gradient algorithms [20, §12] , [14] , [16] , [19] .  ... 
arXiv:1803.10441v1 fatcat:kzpw6lfn3raobimf3sfyi24sti

Distributed Nash Equilibrium Seeking for Noncooperative Games of High-Order Nonlinear Multi-Agent Systems Over Weight-Unbalanced Digraphs [article]

Zhenhua Deng, Jin Luo
2021 arXiv   pre-print
In order to seek the Nash equilibrium of the noncooperative games, we propose two distributed algorithms based on state feedback and output feedback, respectively.  ...  Due to the high-order nonlinear dynamics and the weight-unbalanced digraphs, existing Nash equilibrium seeking algorithms cannot solve our problem.  ...  Deng, Distributed Nash equilibrium seeking for aggregative Distributed consensus-based economic dispatch with transmis- games with second-order nonlinear players, Automatica 135  ... 
arXiv:2112.08744v1 fatcat:li7nag434rc4xahdeb2owxioya

Joint Strategy Fictitious Play With Inertia for Potential Games

Jason R. Marden, GÜrdal Arslan, Jeff S. Shamma
2009 IEEE Transactions on Automatic Control  
We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games.  ...  ., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted  ...  A profile of actions is called a pure Nash equilibrium 1 if, for all players (1) We will consider the class of games known as "generalized ordinal potential games", defined as follows.  ... 
doi:10.1109/tac.2008.2010885 fatcat:kr3dg42xuvhzldd4ogujfvyic4

Differentially private Nash equilibrium seeking for networked aggregative games [article]

Maojiao Ye, Guoqiang Hu, Lihua Xie, Shengyuan Xu
2019 arXiv   pre-print
This paper considers the privacy-preserving Nash equilibrium seeking strategy design for a class of networked aggregative games, in which the players' objective functions are considered to be sensitive  ...  By synthesizing the perturbed average consensus protocol with a gradient algorithm, distributed privacy-preserving Nash equilibrium seeking strategies are established for the aggregative games under both  ...  Motivated by the wide applications of aggregative games in distributed systems, Nash equilibrium seeking for aggregative games on communication graphs is attracting increasing attention in recent years  ... 
arXiv:1911.10514v1 fatcat:ezzh4louq5bftky6ijxxtithpm

Designing pricing strategies for coordination of networked distributed energy resources

Bahman Gharesifard, Tamer Basar, Alejandro D. Domínguez-García
2014 IFAC Proceedings Volumes  
a Nash equilibrium solution in a distributed manner.  ...  The aggregator and DERs' strategic decision-making process can be cast as a Stackelberg game, in which aggregator acts as the leader and the DERs are the followers.  ...  The existence of a (pure) Nash equilibrium for this class of games is guaranteed [Rosen, 1965] .  ... 
doi:10.3182/20140824-6-za-1003.00623 fatcat:672aci6yi5cfxbn2dmlvrdwc5e

Privacy and Truthful Equilibrium Selection for Aggregative Games [chapter]

Rachel Cummings, Michael Kearns, Aaron Roth, Zhiwei Steven Wu
2015 Lecture Notes in Computer Science  
We study a very general class of games -multi-dimensional aggregative games -which in particular generalize both anonymous games and weighted congestion games.  ...  We also give similar results for a related class of one-dimensional games with weaker conditions on the aggregation function, and apply our main results to a multi-dimensional market game.  ...  mediated game, thus implementing a Nash equilibrium of the underlying game of complete information.  ... 
doi:10.1007/978-3-662-48995-6_21 fatcat:occevmfknnenjpwp37qwf3c4ku

Privacy and Truthful Equilibrium Selection for Aggregative Games [article]

Rachel Cummings, Michael Kearns, Aaron Roth, Zhiwei Steven Wu
2015 arXiv   pre-print
We study a very general class of games --- multi-dimensional aggregative games --- which in particular generalize both anonymous games and weighted congestion games.  ...  Nash equilibrium of the induced complete information game.  ...  strategy) an ex-post Nash equilibrium in the mediated version of any aggregative game, thus implementing a Nash equilibrium of the underlying game of complete information.  ... 
arXiv:1407.7740v3 fatcat:5ynqbsnijbbpdd5hscudjfxm6a

Continuous-time integral dynamics for a class of aggregative games with coupling constraints

Claudio De Persis, Sergio Grammatico
2019 IEEE Transactions on Automatic Control  
We consider continuous-time equilibrium seeking in a class of aggregative games with strongly convex cost functions and affine coupling constraints.  ...  We propose simple, semi-decentralized integral dynamics and prove their global asymptotic convergence to a variational generalized aggregative or Nash equilibrium.  ...  Our contribution is complementary to that in [14] , which proposes continuous-time, distributed dynamics for generalized Nash equilibrium seeking in aggregative games with coupling equality constraints  ... 
doi:10.1109/tac.2019.2939639 fatcat:vyoyf4s24zeyrlsellflo7dcku

Random Access Game and Medium Access Control Design

Lijun Chen, S H Low, J C Doyle
2010 IEEE/ACM Transactions on Networking  
We characterize Nash equilibria of random access games, study their dynamics, and propose distributed algorithms (strategy evolutions) to achieve Nash equilibria.  ...  We thus propose a novel medium access method derived from carrier sense multiple access/collision avoidance (CSMA/CA) according to distributed strategy update mechanism achieving the Nash equilibrium of  ...  Hence, the gradient play (13) converges to the unique Nash equilibrium of random access game . Theorem 8 guarantees the convergence of distributed gradient play to the Nash equilibrium.  ... 
doi:10.1109/tnet.2010.2041066 fatcat:pzhzgbzdwfalxlzc32wx4k2r7i

Distributed optimization for aggregative games based on Euler-Lagrange systems with large delay constraints

Long Zhang, Ge Guo, Ge Guo
2020 IEEE Access  
Finally, a numerical example is used to show the effectiveness and superiority of proposed method. INDEX TERMS Aggregative games, Nash equilibrium, Large delays, Euler-Lagrange systems.  ...  First, a distributed algorithm is put forward to try to find the Nash equilibrium by the deliberated group of Euler-Lagrange systems with "small" delay and "large" delay.  ...  ( 6 ) is close to the Nash equilibrium modelled by the aggregative game (1).  ... 
doi:10.1109/access.2020.3028143 fatcat:6cwopyoqz5exbixgixmok65qv4

Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking [article]

Tatiana Tatarenko, Wei Shi, Angelia Nedich
2018 arXiv   pre-print
We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative convex games with strongly monotone mappings.  ...  Using the reformulation of the Nash equilibrium problem based on the strong monotone augmented game mapping, we prove the convergence of this algorithm to a Nash equilibrium with a geometric rate.  ...  The focus of our paper is on discrete-time algorithms applicable to fast distributed Nash equilibrium seeking in a class of non-cooperative games with strongly monotone mappings.  ... 
arXiv:1809.07383v3 fatcat:wdgzwyap3fhlrjqkb66qtaiosu

Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints [article]

Xin Cai, Feng Xiao, Bo Wei
2021 arXiv   pre-print
To reach the general Nash equilibrium of an aggregative game, a distributed strategy-updating rule is proposed by a combination of the coordination of Lagrange multipliers and the estimation of the aggregator  ...  In this paper, we explore aggregative games over networks of multi-integrator agents with coupled constraints.  ...  A number of distributed algorithms were proposed to seek Nash equilibrium of aggregative games.  ... 
arXiv:2106.10697v1 fatcat:5fcqosm54nejnlursdtu2rry54

Game couplings: Learning dynamics and applications

Maria-Florina Balcan, Florin Constantin, Georgios Piliouras, Jeff S. Shamma
2011 IEEE Conference on Decision and Control and European Control Conference  
Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm.  ...  Game coupling intuitively allows us to stitch together the payoff structures of two or more games into a new game.  ...  This work was supported by NSF grants CCF-0953192 and CCF-1101215, by ONR grant N00014-09-1-0751, by AFOSR grant FA9550-09-1-0538, and by a Microsoft Research Faculty Fellowship.  ... 
doi:10.1109/cdc.2011.6161365 dblp:conf/cdc/BalcanCPS11 fatcat:xatrmvpnzfhm7oxx4rnxuodb7y
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