State based potential games

Marden, Jason R.

doi:10.1016/j.automatica.2012.08.037

Cited by 145 publications

(111 citation statements)

References 38 publications

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“…Confined to such local agent utility functions, Gopalakrishnan et al (103) derived the complete set of local agent utility functions that ensure the existence of a pure Nash equilibrium; however, optimizing over such utility functions to optimize the price of anarchy is very much an open question, as highlighted above. Other recent work (104)(105)(106) has introduced a state in the game environment as a design parameter to design player objective functions of a desired locality.…”

Section: As01ch02_shammamentioning

confidence: 99%

Game Theory and Control

Marden

Shamma

2018

Annu. Rev. Control Robot. Auton. Syst.

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Game theory is the study of decision problems in which there are multiple decision makers and the quality of a decision maker's choice depends on both that choice and the choices of others. While game theory has been studied predominantly as a modeling paradigm in the mathematical social sciences, there is a strong connection to control systems in that a controller can be viewed as a decision-making entity. Accordingly, game theory is relevant in settings with multiple interacting controllers. This article presents an introduction to game theory, followed by a sampling of results in three specific control theory topics where game theory has played a significant role: (a) zero-sum games, in which the two competing players are a controller and an adversarial environment; (b) team games, in which several controllers pursue a common goal but have access to different information; and (c) distributed control, in which both a game and online adaptive rules are designed to enable distributed interacting subsystems to achieve a collective objective.

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Section: As01ch02_shammamentioning

confidence: 99%

Game Theory and Control

Marden

Shamma

2018

Annu. Rev. Control Robot. Auton. Syst.

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“…To capture such dynamic aspects of the utility function, we define state-based utility functions [28] as follows.…”

Section: Establishment Cost Exploration Benefit Andmentioning

confidence: 99%

Coevolutionary modeling in network formation

Al‐Shyoukh

Chasparis

Shamma

2014

2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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“…This property has been exploited in many works such as [30], where distributed optimization problems are addressed by using potential games and population dynamics. In [33], a general analysis of statebased potential games is presented and the growing interest in the application of game-theoretic methods to the design and control of multi-agent systems is discussed.Finally, the third motivation for using an EGT approach is that the solution of games can be obtained by employing local information [34], [35]. In [20], local rules are designed in order to achieve a global objective.…”

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The Role of Population Games and Evolutionary Dynamics in Distributed Control Systems: The Advantages of Evolutionary Game Theory

et al. 2017

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Recently, there has been an increasing interest in studying large-scale distributed systems in the control community. Efforts have been invested in developing several techniques wishing to address the main challenges found in this kind of problems, for instance, the amount of information to guarantee the proper operation of the system and the economic costs associated to the required communication structure. Moreover, another issue appears when there is a large amount of required data to control the system. The measuring and transmission processes, and the computation of the control inputs make closed-loop systems suffer from high computational burden.One way to overcome such problems is to consider the use of multi-agent systems framework, which may be cast in game-theoretical terms. Game theory studies interactions between self-interested agents. Particularly, this theory tackles with the problem of interaction between agents using different strategies that wish to maximize their welfares. For instance in [1], the authors provide connections between games, optimization, and learning for signal processing in networks. Other approaches in terms of learning and games can be found in [2]. In [3], distributed computation algorithms are developed based on generalized convex games that do not require full information, and where there is a dynamic change in terms of network topologies. Applications of game theory in control of optical networks and game-theoretic methods for smart grids are described in [4], [5], [6]. Another approach in game theoretical methods is to design protocols or mechanisms that possess some desirable properties [7]. This approach leads to a broad analysis of multi-agent interactions, particularly those involving negotiation and coordination problems [8]. Other game-theoretical applications to engineering are reported in [9].From a game-theoretical perspective, it can be distinguished among three types of games: matrix games, continuous games, and differential/dynamic games (see "The relationship among matricial games, full-potential population games, and resource allocation problems"). In matrix games (that generally use the normal form), individuals play simultaneously and only once, and the decision is mainly based on a static terms. In this case, players or agents are individually treated. Differently, in continuous games, players have infinitely many pure strategies [10], [11]. On the other hand, in dynamic games it is assumed that players can use some type of learning mechanism that allows them to adjust the actions taken based on their past decisions. Basically, it can be said that dynamic games are characterized by three main problems: i) how to model the environment where players interact; ii) how to model the objectives of players; and iii) how to specify the order in which the actions are taken and how much information each player possesses. In this case, it is assumed that there are interactions between large number of agents (which are usually unknown) [12].Among these dynamic game...

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State based potential games

Cited by 145 publications

References 38 publications

Game Theory and Control

Game Theory and Control

Coevolutionary modeling in network formation

The Role of Population Games and Evolutionary Dynamics in Distributed Control Systems: The Advantages of Evolutionary Game Theory

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