Results 1  10
of
96
The complexity of computing a Nash equilibrium
, 2006
"... We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability of n ..."
Abstract

Cited by 329 (23 self)
 Add to MetaCart
We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability of normalform games and graphical games, and shows that these kinds of games can implement arbitrary members of a PPADcomplete class of Brouwer functions. 1
Intrinsic Robustness of the Price of Anarchy
 STOC'09
, 2009
"... The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium ..."
Abstract

Cited by 101 (12 self)
 Add to MetaCart
(Show Context)
The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regretminimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a “canonical sufficient condition ” for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regretminimizing players (or “price of total anarchy”). Smoothness arguments also have automatic implications for the inefficiency of approximate and BayesianNash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomiallength bestresponse sequences. We also identify classes of games — most notably, congestion games with cost functions restricted to an arbitrary fixed set — that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worstcase upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with nonpolynomial cost functions, and the first
Adaptive Heuristics
 Econometrica
, 2005
"... We exhibit a large class of simple rules of behavior, which we call adaptive heuristics, and show that they generate rational behavior in the long run. These adaptive heuristics are based on natural regret measures, and may be viewed as a bridge between rational and behavioral viewpoints. Taken toge ..."
Abstract

Cited by 77 (5 self)
 Add to MetaCart
We exhibit a large class of simple rules of behavior, which we call adaptive heuristics, and show that they generate rational behavior in the long run. These adaptive heuristics are based on natural regret measures, and may be viewed as a bridge between rational and behavioral viewpoints. Taken together, the results presented here establish a solid connection between the dynamic approach of adaptive heuristics and the static approach of correlated equilibria.
On the price of anarchy and stability of correlated equilibria of linear congestion games
, 2005
"... ..."
On the topologies formed by selfish peers
 In PODC ’06
"... Current peertopeer (P2P) systems often suffer from a large fraction of freeriders not contributing any resources to the network. Various mechanisms have been designed to overcome this problem. However, the selfish behavior of peers has aspects which go beyond resource sharing. This paper studies t ..."
Abstract

Cited by 54 (5 self)
 Add to MetaCart
(Show Context)
Current peertopeer (P2P) systems often suffer from a large fraction of freeriders not contributing any resources to the network. Various mechanisms have been designed to overcome this problem. However, the selfish behavior of peers has aspects which go beyond resource sharing. This paper studies the effects on the topology of a P2P network if peers selfishly select the peers to connect to. In our model, a peer exploits locality properties in order to minimize the latency (or response times) of its lookup operations. At the same time, the peer aims at not having to maintain links to too many other peers in the system. We show that the resulting topologies can be much worse than if peers collaborated. Moreover, the network may never stabilize, even in the absence of churn. 1
The complexity of game dynamics: Bgp oscillations, sink equilibria, and beyond
 In SODA ’08: Proceedings of the nineteenth annual ACMSIAM symposium on Discrete algorithms
, 2008
"... We settle the complexity of a wellknown problem in networking by establishing that it is PSPACEcomplete to tell whether a system of path preferences in the BGP protocol [25] can lead to oscillatory behavior; one key insight is that the BGP oscillation question is in fact one about Nash dynamics. W ..."
Abstract

Cited by 34 (4 self)
 Add to MetaCart
(Show Context)
We settle the complexity of a wellknown problem in networking by establishing that it is PSPACEcomplete to tell whether a system of path preferences in the BGP protocol [25] can lead to oscillatory behavior; one key insight is that the BGP oscillation question is in fact one about Nash dynamics. We show that the concept of sink equilibria proposed recently in [11] is also PSPACEcomplete to analyze and approximate for graphical games. Finally, we propose a new equilibrium concept inspired by game dynamics, unit recall equilibria, which we show to be close to universal (exists with high probability in a random game) and algorithmically promising. We also give a relaxation thereof, called componentwise unit recall equilibria, which we show to be both tractable and universal (guaranteed to exist in every game).
Strong Mediated Equilibrium
 In Proceedings of AAAI06
, 2006
"... Providing agents with strategies that will be robust against deviations by coalitions is central to the design of multiagent agents. However, such strategies, captured by the notion of strong equilibrium, rarely exist. This paper suggests the use of mediators in order to enrich the set of situati ..."
Abstract

Cited by 30 (5 self)
 Add to MetaCart
(Show Context)
Providing agents with strategies that will be robust against deviations by coalitions is central to the design of multiagent agents. However, such strategies, captured by the notion of strong equilibrium, rarely exist. This paper suggests the use of mediators in order to enrich the set of situations where we can obtain stability against deviations by coalitions. A mediator is a reliable entity, which can ask the agents for the right to play on their behalf, and is guaranteed to behave in a prespecified way based on messages received from the agents. However, a mediator can not enforce behavior; that is, ∗ An extended abstract of this paper is appearing at the TwentyFirst National Conference on Artificial Intelligence (AAAI06). Almost all proofs are missing from the extended abstract. This Version of the paper contains all of these missing proofs, and provides additional discussions and results. Furthermore, some of the definitions that do appear in the extended abstract have been slightly modified. 1 agents can play in the game directly without the mediator’s help. We prove some general results about mediators, and concentrate on the notion of strong mediated equilibrium; we show that desired behaviors, which are stable against deviations by coalitions, can be obtained using mediators in several class of settings. 1
ActionGraph Games
"... Representing and reasoning with games becomes difficult once they involve large numbers of actions and players, because the space requirement for utility functions can grow unmanageably. ActionGraph Games (AGGs) are a fullyexpressive game representation that can compactly express utility functions ..."
Abstract

Cited by 25 (5 self)
 Add to MetaCart
Representing and reasoning with games becomes difficult once they involve large numbers of actions and players, because the space requirement for utility functions can grow unmanageably. ActionGraph Games (AGGs) are a fullyexpressive game representation that can compactly express utility functions with structure such as contextspecific independence, anonymity, and additivity. We show that AGGs can be used to compactly represent all games that are compact when represented as graphical games, symmetric games, anonymous games, congestion games, and polymatrix games, as well as games that require exponential space under all of these existing representations. We give a polynomialtime algorithm for computing a player’s expected utility under an arbitrary mixedstrategy profile, and show how to use this algorithm to achieve exponential speedups of existing methods for computing sample Nash equilibria. We present results of experiments showing that using AGGs leads to a dramatic increase in the size of games accessible to computational analysis.