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Distributed coverage games for mobile visual sensors (i): Reaching the set of nash equilibria
 In Proc. of the 48th IEEE Conf. on Decision and Control and 28th Chinese Control Conference
, 2009
"... the set of global optima ..."
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Overcoming Limitations of GameTheoretic Distributed Control
"... Abstract—Recently, game theory has been proposed as a tool for cooperative control. Specifically, the interactions of a multiagent distributed system are modeled as a noncooperative game where agents are selfinterested. In this work, we prove that this approach of noncooperative control has limit ..."
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Cited by 12 (5 self)
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Abstract—Recently, game theory has been proposed as a tool for cooperative control. Specifically, the interactions of a multiagent distributed system are modeled as a noncooperative game where agents are selfinterested. In this work, we prove that this approach of noncooperative control has limitations with respect to engineering multiagent systems. In particular, we prove that it is not possible to design budget balanced agent utilities that also guarantee that the optimal control is a Nash equilibrium. However, it is important to realize that gametheoretic designs are not restricted to the framework of noncooperative games. In particular, we demonstrate that these limitations can be overcome by conditioning each player’s utility on additional information, i.e., a state. This utility design fits into the framework of a particular form of stochastic games termed statebased games and is applicable in many application domains. 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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Cited by 10 (2 self)
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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.
DISTRIBUTED COVERAGE GAMES FOR ENERGYAWARE MOBILE SENSOR NETWORKS
"... Abstract. Inspired by current challenges in dataintensive and energylimited 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 dataintensive and energylimited 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
Contribution Games in Networks
, 2010
"... We consider network contribution games, where each agent in a network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a re ..."
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Cited by 6 (4 self)
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We consider network contribution games, where each agent in a network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a reward function for each relationship. Every agent is trying to maximize the reward from all relationships that it is involved in. We consider pairwise equilibriaofthisgame, andcharacterizetheexistence, computationalcomplexity, andquality of equilibrium based on the types of reward functions involved. When all reward functions are concave, we prove that the price of anarchy is at most 2. For convex functions the same only holds under some special but very natural conditions. Another special case extensively treated are minimum effort games, where the reward of a relationship depends only on the minimum effort of any of the participants. In these games, we can show existence of pairwise equilibrium and a price of anarchy of 2 for concave functions and special classes of games with convex functions. Finally, we show tight bounds for approximate equilibria and convergence of dynamics in these games.
Distributed Seeking of Nash Equilibria in Mobile Sensor Networks
"... Abstract — In this paper we consider the problem of distributed convergence to a Nash equilibrium based on minimal information about the underlying noncooperative game. We assume that the players/agents generate their actions based only on measurements of local cost functions, which are corrupted wi ..."
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Abstract — In this paper we consider the problem of distributed convergence to a Nash equilibrium based on minimal information about the underlying noncooperative game. We assume that the players/agents generate their actions based only on measurements of local cost functions, which are corrupted with additive noise. Structural parameters of their own and other players ’ costs, as well as the actions of the other players are unknown. Furthermore, we assume that the agents may have dynamics: their actions can not be changed instantaneously. We propose a method based on a stochastic extremum seeking algorithm with sinusoidal perturbations and we prove its convergence, with probability one, to a Nash equilibrium. We discuss how the proposed algorithm can be adopted for solving coordination problems in mobile sensor networks, taking into account specific motion dynamics of the sensors. The local cost functions can be designed such that some specific overall goal is achieved. We give an example in which each agent/sensor needs to fulfill a locally defined goal, while maintaining connectivity with neighboring agents. The proposed algorithms are illustrated through simulations. I.
Contribution games in social networks
 In Proc. 18th European Symposium on Algorithms (ESA
, 2010
"... We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we u ..."
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Cited by 5 (1 self)
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We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a reward function for each relationship. Every agent is trying to maximize the reward from all relationships that it is involved in. We consider pairwise equilibria of this game, and characterize the existence, computational complexity, and quality of equilibrium based on the types of reward functions involved. For example, when all reward functions are concave, we prove that the price of anarchy is at most 2. For convex functions the same only holds under some special but very natural conditions. A special focus of the paper are minimum effort games, where the reward of a relationship depends onlyonthe minimum effort ofanyofthe participants. Finally, we showtight bounds for approximate equilibria and convergence of dynamics in these games. 1
Barriers to nearoptimal equilibria
 IN PROCEEDINGS OF THE 55TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
"... This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worstcase quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, each moti ..."
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Cited by 3 (3 self)
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This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worstcase quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, each motivated by a different set of problems: congestion, scheduling, and distributed welfare games; welfaremaximization in combinatorial auctions with “blackbox” bidder valuations; and welfaremaximization in combinatorial auctions with succinctly described valuations. The most straightforward use of our lower bound framework is to harness an existing computational or communication lower bound to derive a lower bound on the worstcase price of anarchy (POA) in a class of games. This is a new approach to POA lower bounds, which relies on reductions in lieu of explicit constructions. More generally, the POA lower bounds implied by our framework apply to all classes of games that share the same underlying optimization problem, independent of the details of players’ utility functions. For this reason, our lower bounds are particularly significant for problems of game design — ranging from the design of simple combinatorial auctions to the existence of effective tolls for routing networks — where the goal is to design a game that has only nearoptimal equilibria. For example, our results imply that the simultaneous firstprice auction format is optimal among all “simple combinatorial auctions” in several settings.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
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Cited by 3 (1 self)
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
Restoring Pure Equilibria to Weighted Congestion Games
"... Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on s ..."
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Cited by 2 (1 self)
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Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on sharing costs proportional to players’ weights do not generally have purestrategy Nash equilibria. We propose a new way of assigning costs to players with weights in congestion games that recovers the important properties of the unweighted model. This method is derived from the Shapley value, and it always induces a game with a (weighted) potential function. For the special cases of weighted network costsharing and atomic selfish routing games (with Shapley valuebased cost shares), we prove tight bounds on the price of stability and price of anarchy, respectively.