Games with coupled propagated constraints in optical networks with multi-link topologies

Pan, Yan; Pavel, Lacra

doi:10.1016/j.automatica.2008.11.007

Cited by 50 publications

(37 citation statements)

References 25 publications

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“…where s i (x) is defined in (5). Under appropriate assumptions, the game is one of class G2 and admits a unique inner NE solution, x * .…”

Section: A Qos-based Objectivementioning

confidence: 99%

“…A detailed analysis of an example case is provided next. For a separate but similar example of this formulation we refer to [5]. 1) Example: Consider a single-cell spread-spectrum wireless uplink power control system with M users [22].…”

Section: A Qos-based Objectivementioning

confidence: 99%

“…It incorporates paradigms such as Nash equilibrium and incentive compatibility, can help quantifying individual preferences of decision-makers, and has an inherently distributed nature. Consequently, game theoretic models have been applied to a variety of problem domains ranging from economics to communication networks and security [1]- [5].…”

Section: Introductionmentioning

confidence: 99%

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Nash equilibrium design and optimization

Alpcan

Pavel

2009

2009 International Conference on Game Theory for Networks

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Abstract-The general problem of Nash equilibrium design is investigated from an optimization perspective. Within this context, a specific but fairly broad class of noncooperative games are considered that have been applied to a variety of settings including network congestion control, wireless uplink power control, and optical power control. The Nash equilibrium design problem is analyzed under various knowledge assumptions (full versus limited information) and design objectives (QoS versus utility maximization). Among other results, the "price of anarchy" is shown not to be an inherent feature of games that incorporate pricing mechanisms, but merely a misconception that often stems from arbitrary choice of game parameters. Moreover, a simple linear pricing is sufficient for design of Nash equilibrium according to a chosen global objective for a general class of games and under suitable information assumptions.

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“…where s i (x) is defined in (5). Under appropriate assumptions, the game is one of class G2 and admits a unique inner NE solution, x * .…”

Section: A Qos-based Objectivementioning

confidence: 99%

Section: A Qos-based Objectivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nash equilibrium design and optimization

Alpcan

Pavel

2009

2009 International Conference on Game Theory for Networks

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“…Examples of these include communications [4], [10], bandwidth and spectrum allocation [2], [3] and optical networks [7], [8]. Of note is recent work of Pavel and her coauthors [7] where an extragradient scheme [5] in a deterministic regime, capable of accommodating monotone Nash games. Also of interest is recent work that examines best response schemes in the context of monotone Nash games [10].…”

Section: ])mentioning

confidence: 99%

Distributed iterative regularization algorithms for monotone Nash games

Kannan¹,

Shanbhag²

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper, we consider the development of single-timescale schemes for the distributed computation of Nash equilibria. In general, equilibria associated with convex Nash games over continuous strategy sets are wholly captured by the solution set of a variational inequality. Our focus is on Nash games whose equilibrium conditions are given by monotone variational inequalities, a class referred to as monotone Nash games. Unless suitably strong assumptions (such as strong monotonicity) are imposed on the mapping corresponding to the variational inequality, distributed schemes for computing equilibria often require the solution of a sequence of regularized problems, each of which has a unique solution. Such schemes operate on two timescales and are generally harder to implement in online settings. Motivated by this shortcoming, this work focuses on the development of three single timescale iterative regularization schemes that require precisely one projection step at every iteration. The first is an iterative Tikhonov regularization scheme while the second is an analogously constructed iterative proximal-point method. Both schemes are characterized by the property that the regularization/centering parameter are updated after every iteration, rather than when one has an approximate solution to the regularized problem. Finally, a modified form of the proximal-point scheme is also presented where the weight on the proximal term is updated as well.

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“…However, the approach in [2] is not applicable to our problem due to; e.g, the additional dynamics of vehicle queues, the nonlinearity and non-smoothness of dynamic systems and the presence of state and input constraints. Static games have also been widely used to synthesize decentralized schemes for resource allocation, and a necessarily incomplete reference list includes [1], [13], [16], [21], [23]. Another relevant problem is demand response in the emerging smart grid where customers manage their electricity consumption in response to supply conditions.…”

Section: Introductionmentioning

confidence: 99%

Real-time game theoretic coordination of competitive mobility-on-demand systems

Zhu

2013

2013 American Control Conference

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Abstract-This paper considers competitive mobility-ondemand systems where a group of vehicle sharing companies provide pickup-delivery service in populated areas. The companies, on one hand, want to collectively regulate the traffic of the user queueing network, and on the other hand, aim to maximize their own net profit at each time instant by increasing the user delivery and reducing the transition of empty vehicles. We formulate the strategic interconnection among the companies as a real-time game theoretic coordination problem. We propose an algorithm to achieve vehicle balance and practical regulation of the user queueing network. We quantify the relation between the regulation error and the system parameters (e.g., the maximum variation of the user arrival rates).

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Games with coupled propagated constraints in optical networks with multi-link topologies

Cited by 50 publications

References 25 publications

Nash equilibrium design and optimization

Nash equilibrium design and optimization

Distributed iterative regularization algorithms for monotone Nash games

Real-time game theoretic coordination of competitive mobility-on-demand systems

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