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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 largescale cyberphysical 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 largescale cyberphysical 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 largescale 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: microgrid systems, demandside management, and communications. In each area, the stateoftheart 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.
Potential games are necessary to ensure pure Nash equilibria in cost sharing games
 Mathematics of Operations Research
"... We consider the problem of designing distribution rules to share ‘welfare ’ (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; ho ..."
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We consider the problem of designing distribution rules to share ‘welfare ’ (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; however, a characterization of the space of distribution rules that guarantee the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games, which includes a variety of applications such as facility location, routing, network formation, and coverage games. Given arbitrary local welfare functions W, we prove that a distribution rule guarantees equilibrium existence for all games (i.e., all possible sets of resources, agent action sets, etc.) if and only if it is equivalent to a generalized weighted Shapley value on some ‘ground ’ welfare functions W′, which can be distinct from W. However, if budgetbalance is required in addition to the existence of a Nash equilibrium, then W ′ must be the same as W. We also provide an alternate characterization of this space in terms of ‘generalized’ marginal contributions, which is more appealing from the point of view of computational tractability. A possibly surprising consequence of our result is that, in order to guarantee equilibrium existence in all games with any fixed local welfare functions, it is necessary to work within the class of potential games.
ADAPT: A Game Inspired AttackDefense And Performance Metric Taxonomy
"... Abstract. Game theory has been researched extensively in network security demonstrating an advantage of modeling the interactions between attackers and defenders. Game theoretic defense solutions have continuously evolved in most recent years. One of the pressing issues in composing a game theoreti ..."
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Abstract. Game theory has been researched extensively in network security demonstrating an advantage of modeling the interactions between attackers and defenders. Game theoretic defense solutions have continuously evolved in most recent years. One of the pressing issues in composing a game theoretic defense system is the development of consistent quantifiable metrics to select the best game theoretic defense model. We survey existing game theoretic defense, information assurance, and risk assessment frameworks that provide metrics for information and network security and performance assessment. Coupling these frameworks, we propose a game theoretic approach to attackdefense and performance metric taxonomy (ADAPT). ADAPT uses three classifications of metrics: (i) Attacker, (ii) Defender (iii) Performance. We proffer ADAPT with an attempt to aid game theoretic performance metrics. We further propose a game decision system (GDS) that uses ADAPT to compare competing game models. We demonstrate our approach using a distributed denial of service (DDoS) attack scenario. Keywords: Game Theory, Taxonomy, Security Management INTRODUCTION Game theory has received increased attention from network security researchers, investigating defense solutions. The game theory approach has the advantage of modeling the interactions between attackers and defenders, where players have the ability to analyze other player's behavior. This may enable an administrator to develop better strategic defenses for the system. For instance, when there are many actions available to the attacker and defender, it becomes difficult to develop solution strategies. Hamilton, et al. [1] outlined the areas of game theory which are relevant to information warfare using course of actions with predicted outcomes and whatif scenarios. Jiang, et al. In this paper, we attempt to address limitations in research through the proposed game theoretic attackdefense and performance metric taxonomy (ADAPT), which is a taxonomy of game related metrics. We define a game as the interactions between two players with conflicting goals. In our case these players are the attacker (hacker) and system administrator (defender). Game metrics are a set of tools which are used to measure the various kinds of impact a game model has on each of its players. We classify these game metrics based on their impact on attacker, defender, and the performance of the game model on the system which is being run. Prior research has shown, with the use of game theory, how the interaction should take place based on the strategy and the strategy selected from the game model. In this traditional scenario one game model is assessed relative to a particular attack. He, et al. [6] proposed a Game Theoretical AttackDefense Model (GTADM), similar to ADAPT, that quantifies the probability of threats in constructing a risk assessment framework. We extend these general game theory steps and concepts proposed in He, et al. [6] with the use of ADAPT being able to assess competing game models and select the game model which is suitable for defense. This provides a defender with a preliminary view of multiple game models associated to a particular attack.