Multiagent Learning in Large Anonymous Games

Kash, Ian A.; Friedman, Eric; Halpern, Joseph Y.

doi:10.1613/jair.3213

Cited by 19 publications

(9 citation statements)

References 36 publications

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“…Any λ-Lipschitz k-strategy anonymous game is guaranteed to have an ǫ-approximate pure Nash equilibrium, with ǫ = O(λk) [2,15]. The convergence rate to a Nash equilibrium of best-reply dynamics in the context of two-strategy Lipschitz anonymous games is studied by [3,24]. Moreover, [5] showed that finding a pure equilibrium in anonymous games is easy if the number of strategies is constant w.r.t.…”

Section: Related Workmentioning

confidence: 99%

Query complexity of approximate equilibria in anonymous games

Goldberg

Turchetta²

2017

Journal of Computer and System Sciences

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Abstract. We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is query complexity, that is, how many queries are necessary or sufficient to compute an exact or approximate Nash equilibrium. We show that exact equilibria cannot be found via query-efficient algorithms. We also give an example of a 2-strategy, 3-player anonymous game that does not have any exact Nash equilibrium in rational numbers. However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria. We investigate four sub-classes of anonymous games previously considered by [5,15]. Our main result is a new randomized query-efficient algorithm that finds a O(n −1/4 )-approximate Nash equilibrium queryingÕ(n 3/2 ) payoffs and runs in timeÕ(n 3/2 ). This improves on the running time of pre-existing algorithms for approximate equilibria of anonymous games, and is the first one to obtain an inverse polynomial approximation in poly-time. We also show how this can be utilized as an efficient polynomial-time approximation scheme (PTAS). Furthermore, we prove that Ω(n log n) payoffs must be queried in order to find any ǫ-well-supported Nash equilibrium, even by randomized algorithms.

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Section: Related Workmentioning

confidence: 99%

Query complexity of approximate equilibria in anonymous games

Goldberg

Turchetta²

2017

Journal of Computer and System Sciences

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Section: Related Workmentioning

confidence: 99%

Query Complexity of Approximate Equilibria in Anonymous Games

Goldberg

Turchetta

2015

Web and Internet Economics

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We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is query complexity, that is, how many queries are necessary or sufficient to compute an exact or approximate Nash equilibrium. We show that exact equilibria cannot be found via query-efficient algorithms. We also give an example of a 2-strategy, 3-player anonymous game that does not have any exact Nash equilibrium in rational numbers. However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria. We investigate four sub-classes of anonymous games previously considered by [5, 15]. Our main result is a new randomized query-efficient algorithm that finds a O(n −1/4)-approximate Nash equilibrium querying˜Oquerying˜ querying˜O(n 3/2) payoffs and runs in time˜Otime˜ time˜O(n 3/2). This improves on the running time of pre-existing algorithms for approximate equilibria of anonymous games, and is the first one to obtain an inverse polynomial approximation in poly-time. We also show how this can be utilized as an efficient polynomial-time approximation scheme (PTAS). Furthermore, we prove that Ω(n log n) payoffs must be queried in order to find any ǫ-well-supported Nash equilibrium, even by randomized algorithms.

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“…"Sink" equilibria are studied in (Goemans et al, 2005, Mirrokni andSkopalik, 2009). 4 This case is studied in Quint et al (1997) for 2-player games and in Kash et al (2011) for anonymous games. 5 There are, of course, many other possible playing sequences.…”

Section: Introductionmentioning

confidence: 99%

Best-response dynamics, playing sequences, and convergence to equilibrium in random games

Heinrich¹,

Jang²,

Mungo³

et al. 2021

Preprint

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We show that the playing sequence-the order in which players update their actions-is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random n-player m-action games under three distinct playing sequences: clockwork sequences (players take turns according to a fixed cyclic order), random sequences, and simultaneous updating by all players. We analytically characterize the convergence properties of the clockwork sequence best-response dynamic. Our key asymptotic result is that this dynamic almost never converges to a pure Nash equilibrium when n and m are large. By contrast, the random sequence bestresponse dynamic converges almost always to a pure Nash equilibrium when one exists and n and m are large. The clockwork best-response dynamic deserves particular attention: we show through simulation that, compared to random or simultaneous updating, its convergence properties are closest to those exhibited by three popular learning rules that have been calibrated to human game-playing in experiments (reinforcement learning, fictitious play, and replicator dynamics).

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Multiagent Learning in Large Anonymous Games

Cited by 19 publications

References 36 publications

Query complexity of approximate equilibria in anonymous games

Query complexity of approximate equilibria in anonymous games

Query Complexity of Approximate Equilibria in Anonymous Games

Best-response dynamics, playing sequences, and convergence to equilibrium in random games

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