Results 1 
3 of
3
Risk Sensitivity of Price of Anarchy under Uncertainty
, 2013
"... In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertai ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertainty. We establish a connection between the two that provides a novel analytic framework for proving tight performance guarantees for distributed systems in uncertain environments. We present applications of this framework to novel variants of atomic congestion games with uncertain costs, for which we provide tight performance bounds under a wide range of risk attitudes. Our results establish that the individualâ€™s attitude towards uncertainty has a critical effect on system performance and should therefore be a subject of close and systematic investigation.
Robust Price of Anarchy Bounds via LP and Fenchel Duality
"... Bounding the price of anarchy (PoA), which quantifies the degradation in the quality of outcomes in a (pure) Nash equilibrium of a game, is one of the fundamental questions in computational game theory. However, for a large class of games, a pure NE may not always exist and hence a natural question ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Bounding the price of anarchy (PoA), which quantifies the degradation in the quality of outcomes in a (pure) Nash equilibrium of a game, is one of the fundamental questions in computational game theory. However, for a large class of games, a pure NE may not always exist and hence a natural question to pursue is to quantify the inefficiency for weaker notions of equilibrium such as mixed Nash equilibrium, correlated equilibrium or coarse correlated equilibrium, all of which are known to exist for finite games. Several techniques have been developed for bounding the price of anarchy, yet, only a handful of them are applicable for proving the PoA bounds for general equilibrium concepts. Most notable among such techniques is Roughgardenâ€™s elegant smoothness framework, which led to the concept of robust price of anarchy. The term refers to the inefficiency bounds applicable to general equilibrium notions such
Limited Lookahead in ImperfectInformation Games
"... Limited lookahead has been studied for decades in perfectinformation games. This paper initiates a new direction via two simultaneous deviation points: generalization to imperfectinformation games and a gametheoretic approach. The question of how one should act when facing an opponent whose l ..."
Abstract
 Add to MetaCart
Limited lookahead has been studied for decades in perfectinformation games. This paper initiates a new direction via two simultaneous deviation points: generalization to imperfectinformation games and a gametheoretic approach. The question of how one should act when facing an opponent whose lookahead is limited is studied along multiple axes: lookahead depth, whether the opponent(s), too, have imperfect information, and how they break ties. We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPADhard or NPhard. We proceed to design algorithms for computing optimal commitment strategies for when the opponent breaks ties 1) favorably, 2) according to a fixed rule, or 3) adversarially. The impact of limited lookahead is then investigated experimentally. The limitedlookahead player often obtains the value of the game if she knows the expected values of nodes in the game tree for some equilibrium, but we prove this is not sufficient in general. Finally, we study the impact of noise in those estimates and different lookahead depths. This uncovers a lookahead pathology. 1