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32
Learning Efficient Nash Equilibria in Distributed Systems
, 2010
"... Abstract. An individual’s learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic n-person games that possess at l ..."
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Abstract. An individual’s learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: i) the sum of payoffs over all agents, and ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games. JEL: C72, C73 1 1. Learning equilibrium in complex interactive systems Game theory has traditionally focussed on situations that involve a small number of players. In these environments it makes sense to assume that players know the structure of the game and can predict the strategic behavior of their opponents. But there are many situations involving huge numbers of players where these assumptions are not particularly persuasive.
1 Opportunistic Spectrum Access in Cognitive Radio Networks: When to Turn off the Spectrum Sensors
"... Abstract — In cognitive radio networks, spectrum sensing is a critical to both protecting the primary users and creating spectrum access opportunities of secondary users. Channel sensing itself, including active probing and passive listening, often incurs cost, in terms of time overhead, energy cons ..."
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Abstract — In cognitive radio networks, spectrum sensing is a critical to both protecting the primary users and creating spectrum access opportunities of secondary users. Channel sensing itself, including active probing and passive listening, often incurs cost, in terms of time overhead, energy consumption, or intrusion to primary users. It is thus not desirable to sense the channel arbitrarily. In this paper, we are motivated to consider the following problem. A secondary user, equipped with spectrum sensors, dynamically accesses a channel. If it transmits without/with colliding with primary users, a certain reward/penalty is obtained. If it senses the channel, accurate channel information is obtained, but a given channel sensing cost incurs. The third option for the user is to turn off the sensor/transmitter and go to sleep mode, where no cost/gain incurs. So when should the secondary user transmit, sense, or sleep, to maximize the total gain? We derive the optimal transmitting, sensing, and sleeping structure, which is a threshold-based policy. Our work sheds light on designing sensing and transmitting scheduling protocols for cognitive radio networks, especially the in-band sensing mechanism in 802.22 networks. I.
Collaborative sensing in a distributed ptz camera network,” Image Processing
- IEEE Transactions on
, 2012
"... Abstract—The performance of dynamic scene algorithms often suffers because of the inability to effectively acquire features on the targets, particularly when they are distributed over a wide field of view. In this paper, we propose an integrated analysis and control framework for a pan, tilt, zoom ( ..."
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Abstract—The performance of dynamic scene algorithms often suffers because of the inability to effectively acquire features on the targets, particularly when they are distributed over a wide field of view. In this paper, we propose an integrated analysis and control framework for a pan, tilt, zoom (PTZ) camera network in order to maximize various scene understanding performance criteria (e.g., tracking accuracy, best shot, and image resolution) through dynamic camera-to-target assignment and efficient feature acquisition. Moreover, we consider the situation where processing is distributed across the network since it is often unrealistic to have all the image data at a central location. In such situations, the cameras, although autonomous, must collaborate among themselves because each camera’s PTZ parameter entails constraints on the others. Motivated by recent work in cooperative control of sensor networks, we propose a distributed optimization strategy, which can be modeled as a game involving the cameras and targets. The cameras gain by reducing the error covariance of the tracked targets or through higher resolution feature acquisition, which, however, comes at the risk of losing the dynamic target. Through the optimization of this reward-versus-risk tradeoff, we are able to control the PTZ parameters of the cameras and assign them to targets dynamically. The tracks, upon which the control algorithm is dependent, are obtained through a consensus estimation algorithm whereby cameras can arrive at a consensus on the state of each target through a negotiation strategy. We analyze the performance of this collaborative sensing strategy in active camera networks in a simulation environment, as well as a real-life camera network. Index Terms—Camera networks, cooperative camera control, distributed estimation, game theory, video analysis. I.
Decoupling Coupled Constraints Through Utility Design
"... The central goal in multiagent systems is to engineer a decision making architecture where agents make independent decisions in response to local information while ensuring that the emergent global behavior is desirable with respect to a given system level objective. In many systems this control de ..."
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The central goal in multiagent systems is to engineer a decision making architecture where agents make independent decisions in response to local information while ensuring that the emergent global behavior is desirable with respect to a given system level objective. In many systems this control design is further complicated by coupled constraints on the agents’ behavior. This paper seeks to address the design of such algorithms using the field of game theory. In particular, we derive a systematic methodology for designing local agent utility functions such that (i) all resulting pure Nash equilibria of the designed game optimize the given system level objective and satisfy the given coupled constraint (ii) the resulting game possesses an inherent structure that can be exploited in distributed learning, e.g., potential games. Such developments would greatly simplify the control design by eliminating the need to explicitly consider the constraint. One key to this realization is introducing an estimate of the coupled constraint and incorporating exterior penalty functions and barrier functions into the design of the agents’ utility functions.
Game theoretic methods for the smart grid
- IEEE Signal Processing Magazine. Special Issue: Signal Processing Techniques for Smart Grid
"... Abstract The future smart grid is envisioned as a large-scale cyber-physical system encompassing advanced power, communications, control, and computing technologies. In order to accommodate these technologies, it will have to build on solid mathematical tools that can ensure an efficient and robust ..."
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Abstract The future smart grid is envisioned as a large-scale cyber-physical system encompassing advanced power, communications, control, and computing technologies. In order to accommodate these technologies, it will have to build on solid mathematical tools that can ensure an efficient and robust operation of such heterogeneous and large-scale cyberphysical systems. In this context, this paper is an overview on the potential of applying game theory for addressing relevant and timely open problems in three emerging areas that pertain to the smart grid: micro-grid systems, demand-side management, and communications. In each area, the state-of-the-art contributions are gathered and a systematic treatment, using game theory, of some of the most relevant problems for future power systems is provided. Future opportunities for adopting game theoretic methodologies in the transition from legacy systems toward smart and intelligent grids are also discussed. In a nutshell, this article provides a comprehensive account of the application of game theory in smart grid systems tailored to the interdisciplinary characteristics of these systems that integrate components from power systems, networking, communications, and control.
DISTRIBUTED COVERAGE GAMES FOR ENERGY-AWARE MOBILE SENSOR NETWORKS
"... Abstract. Inspired by current challenges in data-intensive and energy-limited sensor networks, we formulate a coverage optimization problem for mobile sensors as a (constrained) repeated multiplayer game. Each sensor tries to optimize its own coverage while minimizing the processing/energy cost. The ..."
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Abstract. Inspired by current challenges in data-intensive and energy-limited sensor networks, we formulate a coverage optimization problem for mobile sensors as a (constrained) repeated multiplayer game. Each sensor tries to optimize its own coverage while minimizing the processing/energy cost. The sensors are subject to the informational restriction that the environmental distribution function is unknown a priori. We present two distributed learning algorithms where each sensor only remembers its own utility values and actions played during the last plays. These algorithms are proven to be convergent in probability to the set of (constrained) Nash equilibria and global optima of certain coverage performance metric, respectively. Numerical examples are provided to verify the performance of our proposed algorithms. 1. Introduction. There
Cooperative topology control with adaptation for improved lifetime in wireless ad hoc networks
- in Proc. IEEE INFOCOM
, 2012
"... Topology control algorithms allow each node in a wireless multi-hop network to adjust the power at which it makes its transmissions and choose the set of neighbors with which it communicates directly, while preserving global goals such as connectivity or coverage. This allows each node to conserve e ..."
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Topology control algorithms allow each node in a wireless multi-hop network to adjust the power at which it makes its transmissions and choose the set of neighbors with which it communicates directly, while preserving global goals such as connectivity or coverage. This allows each node to conserve energy and contribute to increasing the lifetime of the network. In this paper, in contrast to most previous work, we consider (i) both the energy costs of communication as well as the amount of available energy at each node, (ii) the realistic situation of varying rates of energy consumption at different nodes, and (iii) the fact that co-operation between nodes, where some nodes make a sacrifice by increasing energy consumption to help other nodes reduce their consumption, can be used to extend network lifetime. This paper introduces a new distributed topology control algorithm, called the Cooperative Topology Control with Adaptation (CTCA), based on a game-theoretic approach that maps the problem of maximizing the network’s lifetime into an ordinal potential game. We prove the existence of a Nash equilibrium for the game. Our simulation results indicate that the CTCA algorithm extends the life of a network by more than 50 % compared to the best previously-known algorithm. We also study the performance of the distributed CTCA algorithm in comparison to an optimal centralized algorithm as a function of the communication ranges of nodes and node density. ar X iv
Game Couplings: Learning Dynamics and Applications
"... Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is ..."
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Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is formally known about their properties and global dynamics. We investigate such distributed systems by introducing a novel game-theoretic construct, that we call game-coupling. Game coupling intuitively allows us to stitch together the payoff structures of sub-games. In order to study efficiency issues, we extend the price of anarchy approach (a major focus of gametheoretical multi-agent systems [22]) to this setting, where we now care about the performance of each individual subsystem as well as the global performance. Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm. We prove matching welfare guarantees for both, both for individual subsystems as well as for the global system, using a generalization of the (λ, µ)-smoothness framework [19]. In the second part of the paper, we work on understanding conditions that allow for well-structured couplings. More generally, we examine when do game couplings preserve or enhance desirable properties of the original games, such as convergence of best response dynamics and low price of anarchy.
Game theory for signal processing in networks,”
- IEEE Signal Process. Mag.,
, 2015
"... Abstract In this tutorial, the basics of game theory are introduced along with an overview of its most recent and emerging applications in signal processing. One of the main features of this contribution is to gather in a single paper some fundamental game-theoretic notions and tools which, over th ..."
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Abstract In this tutorial, the basics of game theory are introduced along with an overview of its most recent and emerging applications in signal processing. One of the main features of this contribution is to gather in a single paper some fundamental game-theoretic notions and tools which, over the past few years, have become widely spread over a large number of papers. In particular, both strategic-form and coalition-form games are described in details while the key connections and differences between them are outlined. Moreover, a particular attention is also devoted to clarify the connections between strategic-form games and distributed optimization and learning algorithms. Beyond an introduction to the basic concepts and main solution approaches, several carefully designed examples are provided to allow a better understanding of how to apply the described tools.
Learning in Network Games with Incomplete Information
"... © istockphoto.com/jamie farrant [Asymptotic analysis and tractable implementation of rational behavior] The role of social networks in learning and opinion formation has been demonstrated in a variety of scenarios such as the dynamics of technology adoption [1], consumption behavior [2], organizatio ..."
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© istockphoto.com/jamie farrant [Asymptotic analysis and tractable implementation of rational behavior] The role of social networks in learning and opinion formation has been demonstrated in a variety of scenarios such as the dynamics of technology adoption [1], consumption behavior [2], organizational behavior [3], and financial markets [4]. The emergence of network-wide social phenomena from local interactions between connected agents has been studied using field data [5]–[7] as well as lab experiments [8], [9]. Interest in opinion dynamics over networks is further amplified by the continuous growth in the amount of time that individuals spend on social media Web sites and the consequent increase in the importance of networked phenomena in social and economic outcomes. As quantitative data
