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25
Routing without regret: On convergence to nash equilibria of regretminimizing algorithms in routing games
 In PODC
, 2006
"... Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging envi ..."
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Cited by 48 (6 self)
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Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question: if each player in a routing game uses a noregret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games havesubstantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimalagents, behavior will approach Nash equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that dependspolynomially on the players ' regret bounds and the maximum slope of any latency function. We also show that priceofanarchy results may be applied to these approximate equilibria, and alsoconsider the finitesize (noninfinitesimal) loadbalancing model of Azar [2].
Correlated Equilibrium in Access Control for Wireless Communications”, Networking 2006
, 2006
"... Abstract. We study a finite population of mobiles communicating using the slotted ALOHAtype protocol. Our objective is the study of coordination between the mobiles in both cooperative as well as noncooperative scenarios. Our study is based on the correlated equilibrium concept, a notion introduce ..."
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Cited by 14 (4 self)
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Abstract. We study a finite population of mobiles communicating using the slotted ALOHAtype protocol. Our objective is the study of coordination between the mobiles in both cooperative as well as noncooperative scenarios. Our study is based on the correlated equilibrium concept, a notion introduced by Aumann that broadens the Nash equilibrium. We study ways in which signaling can improve the performance both in the cooperative as well as in the noncooperative cases, even in the absence of any extra information being conveyed through these signals. 1
NonAtomic Games for MultiUser Systems
"... In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel ..."
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Cited by 11 (5 self)
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In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the matched filter, the MMSE filter and the optimum filter. The goal of this paper is to extend previous work, and to derive simple expressions for the noncooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of nonatomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.
Dynamic Discrete Power Control in Cellular Networks
"... We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to ..."
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Cited by 6 (3 self)
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We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: (i) the case of full state information and (ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as noncooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of bestresponse policies in the noncooperative case. We present an algorithm to compute equilibria policies in the case of two noncooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of another mobile. Our results are illustrated and validated through various numerical examples. I
Flows and Decompositions of Games: Harmonic and Potential Games
"... In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze na ..."
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Cited by 4 (2 self)
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In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the wellknown potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the
NearOptimal Power Control in Wireless Networks: A Potential Game Approach
"... We study power control in a multicell CDMA wireless system whereby selfinterested users share a common spectrum and interfere with each other. Our objective is to design a power control scheme that achieves a (near) optimal power allocation with respect to any predetermined network objective (suc ..."
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Cited by 3 (3 self)
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We study power control in a multicell CDMA wireless system whereby selfinterested users share a common spectrum and interfere with each other. Our objective is to design a power control scheme that achieves a (near) optimal power allocation with respect to any predetermined network objective (such as the maximization of sumrate, or some fairness criterion). To obtain this, we introduce the potentialgame approach that relies on approximating the underlying noncooperative game with a “close ” potential game, for which prices that induce an optimal power allocation can be derived. We use the proximity of the original game with the approximate game to establish through Lyapunovbased analysis that natural userupdate schemes (applied to the original game) converge within a neighborhood of the desired operating point, thereby inducing nearoptimal performance in a dynamical sense. Additionally, we demonstrate through simulations that the actual performance can in practice be very close to optimal, even when the approximation is inaccurate. As a concrete example, we focus on the sumrate objective, and evaluate our approach both theoretically and empirically.
Affective DecisionMaking: A Theory of OptimismBias
, 2010
"... Optimismbias is inconsistent with the independence of decision weights and payoffs found in models of choice under risk, such as expected utility theory and prospect theory. Hence, to explain the evidence suggesting that agents are optimistically biased, we propose an alternative model of risky cho ..."
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Cited by 2 (0 self)
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Optimismbias is inconsistent with the independence of decision weights and payoffs found in models of choice under risk, such as expected utility theory and prospect theory. Hence, to explain the evidence suggesting that agents are optimistically biased, we propose an alternative model of risky choice, affective decisionmaking, where decision weights — which we label affective or perceived risk — are endogenized. Affective decision making (ADM) is a strategic model of choice under risk, where we posit two cognitive processes: the “rational” and the “emotional” processes. The two processes interact in a simultaneousmove intrapersonal potential game, and observed choice is the result of a pure strategy Nash equilibrium in this potential game. We show that regular ADM potential games have an odd number of locally unique pure strategy Nash equilibria, and demonstrate this …nding for a¤ective decision making in insurance markets. We prove that ADM potential games are refutable, by axiomatizing the ADM potential maximizers.