Regret minimization and the price of total anarchy

Blum, Avrim; Hajiaghayi, MohammadTaghi; Ligett, Katrina; Roth, Aaron

doi:10.1145/1374376.1374430

Cited by 114 publications

(196 citation statements)

References 33 publications

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“…Numerous articles study the convergence rate of best-response dynamics to approximately optimal solutions [16,24,4,10]. For example, polynomial-time bounds has been proven for the speed of convergence to approximately optimal solutions for approximate Nash dynamics in a large class of potential games [4], and for learning-based regret-minimisation dynamics for valid-utility games [10].…”

Section: Background and Related Workmentioning

confidence: 99%

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A Theoretical Examination of Practical Game Playing: Lookahead Search

Mirrokni

Thain

Vetta

2012

Algorithmic Game Theory

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Abstract. Lookahead search is perhaps the most natural and widely used game playing strategy. Given the practical importance of the method, the aim of this paper is to provide a theoretical performance examination of lookahead search in a wide variety of applications.To determine a strategy play using lookahead search, each agent predicts multiple levels of possible re-actions to her move (via the use of a search tree), and then chooses the play that optimizes her future payoff accounting for these re-actions. There are several choices of optimization function the agents can choose, where the most appropriate choice of function will depend on the specifics of the actual game -we illustrate this in our examples. Furthermore, the type of search tree chosen by computationally-constrained agent can vary. We focus on the case where agents can evaluate only a bounded number, k, of moves into the future. That is, we use depth k search trees and call this approach k-lookahead search.We apply our method in five well-known settings: industrial organization (Cournot's model); AdWord auctions; congestion games; valid-utility games and basic-utility games; cost-sharing network design games. We consider two questions. First, what is the expected social quality of outcome when agents apply lookahead search? Second, what interactive behaviours can be exhibited when players use lookahead search?Myopic game playing (whose corresponding equilibria are Nash equilibria), where each player can only foresee the immediate effect of her own actions, is the special case of 1-lookahead search. Thus, for the first question, it is natural to ask whether social outcomes improve when players use more foresight than in myopic behaviour. The answer depends on the game played: (i) For the Cournot game, applying 2-lookahead leads to a 12.5% increase in output and a 5.5% increase in social surplus compared with myopic competition. Similar bounds arise as the length k of foresight increases.(ii) In AdWord auctions (or generalized second-price auctions), we show that 2-lookahead game playing results in outcomes that are always optimal to within a constant factor; in contrast, myopic game play can produce arbitrarily poor equilibrium outcomes.(ii) For congestion games, as with myopic game playing, lookahead search leads to constant factor qualitative guarantees. (iv) For basic-utility games, on the other hand, whilst myopic game playing always leads to constant factor approximations, additional foresight can lead to arbitrarily bad solutions! (v) In a simple Shapley network design game, qualitative guarantees improve with the length of foresight. Regarding the second question, a variety of interesting game playing characteristics also arise with lookahead search. Stackelberg leader-follower behaviours can be induced when the players have asymmetric computational power. For example, Stackelberg equilibria can be produced in the Cournot game. Lookahead search can also generate "uncoordinated" cooperative behaviour!

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Section: Background and Related Workmentioning

confidence: 99%

“…In many other models the effect of learning algorithms [81] is examined, for example, regret minimisation dynamics [26,33,34,11,9,10,20] and fictitious play [12]. In most of these studies the most important factor is the stability of equilibria, and not measurements of the social value of equilibria.…”

Section: Background and Related Workmentioning

confidence: 99%

A Theoretical Examination of Practical Game Playing: Lookahead Search

Mirrokni

Thain

Vetta

2012

Algorithmic Game Theory

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“…We model Byzantine players who may behave arbitrarily by using the no-regret framework recently introduced by Blum et al [5] to bound the price of total anarchy. The price of total anarchy compares the average social cost over T rounds of repeated play to the cost of the optimal flow, when the rational players have no regret.…”

Section: Introductionmentioning

confidence: 99%

The Price of Malice in Linear Congestion Games

Roth

2008

Lecture Notes in Computer Science

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We study the price of malice in linear congestion games using the technique of no-regret analysis in the presence of Byzantine players. Our assumptions about the behavior both of rational players, and of malicious players are strictly weaker than have been previously used to study the price of malice. Rather than assuming that rational players route their flow according to a Nash equilibrium, we assume only that the play so as to have no regret. Rather than assuming that malicious players myopically seek to maximize the social cost of the game, we study Byzantine players about whom we make no assumptions, who may be seeking to optimize any utility function, and who may engage in an arbitrary degree of counterspeculation. Because our assumptions are strictly weaker than in previous work, the bounds we prove on two measures of the price of malice hold also for the quantities studied by Babaioff et al. [2] and Moscibroda et al. [17] We prove tight bounds both for the special case of parallel link routing games, and for general congestion games.

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“…Remarkably, such approximation bounds hold in interesting classes of games, including in selfish routing networks. See [2,6,19] for initial formalizations of this approach, and [36] for a recent general result that shows that, under weak conditions, POA bounds for equilibria extend automatically to the results of repeated experimentation.…”

Section: (B)mentioning

confidence: 99%

“…But a number of new types of worst-case guarantees, coupled with novel behavioral models, have already begun to sprout in the AGT literature. For example: mechanism implementation in undominated strategies [3] and in ex post collusion-proof Nash equilibrium [31]; the price of total anarchy [6,36]; and the complexity of unit-recall games [16]. We expect that these are only the vanguard of what promises to be a rich and relevant theory.…”

Section: Future Directionsmentioning

confidence: 99%

Algorithmic Game Theory

Persiano¹

2011

Lecture Notes in Computer Science

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Regret minimization and the price of total anarchy

Cited by 114 publications

References 33 publications

A Theoretical Examination of Practical Game Playing: Lookahead Search

A Theoretical Examination of Practical Game Playing: Lookahead Search

The Price of Malice in Linear Congestion Games

Algorithmic Game Theory

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