Computing Nash Equilibria of Action-Graph Games via Support Enumeration

Thompson, David R. M.; Leung, Samantha; Leyton‐Brown, Kevin

doi:10.1007/978-3-642-25510-6_29

“…For multi-slot UWR auctions, this can have an unexpected side effect: it can be impossible for a high-quality advertiser to win the second position. the pure strategy Nash equilibria of an AGG [Porter et al 2008;Thompson et al 2011].…”

Section: Second Analysis: All Pure Nash Equilibriamentioning

confidence: 99%

Revenue optimization in the generalized second-price auction

Thompson

¹

,

Leyton‐Brown

²

2013

Proceedings of the Fourteenth ACM Conference on Electronic Commerce

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We consider the optimization of revenue in advertising auctions based on the generalized second-price (GSP) paradigm, which has become a de facto standard. We examine several different GSP variants (including squashing and different types of reserve prices), and consider how to set their parameters optimally. One intriguing finding is that charging each advertiser the same per-click reserve price ("unweighted reserve prices") yields dramatically more revenue than the quality-weighted reserve prices that have become common practice. This result is robust, arising both from theoretical analysis and from two different kinds of computational experiments. We also identify a new GSP variant that is revenue optimal in restricted settings. Finally, we study how squashing and reserve prices interact, and how equilibrium selection affects the revenue of GSP when features such as reserves or squashing are applied.

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“…Leyton-Brown 2009]. Further, using support enumeration, it is possible to enumerate all 4 the pure strategy Nash equilibria of an AGG [Porter et al 2008;Thompson et al 2011]. For this set of experiments we used a uniform distribution 5 over settings: drawing each agent's valuation from U (0, 25), each agent's quality score from U (0, 1), and α k+1 from U (0, α k ).…”

Section: Second Analysis: All Pure Nash Equilibriamentioning

confidence: 99%

Revenue optimization in the generalized second-price auction

Thompson

¹

,

Leyton‐Brown

²

2013

Proceedings of the Fourteenth ACM Conference on Electronic Commerce

Self Cite

View full text Add to dashboard Cite

We consider the optimization of revenue in advertising auctions based on the generalized second-price (GSP) paradigm, which has become a de facto standard. We examine several different GSP variants (including squashing and different types of reserve prices), and consider how to set their parameters optimally. One intriguing finding is that charging each advertiser the same per-click reserve price ("unweighted reserve prices") yields dramatically more revenue than the quality-weighted reserve prices that have become common practice. This result is robust, arising both from theoretical analysis and from two different kinds of computational experiments. We also identify a new GSP variant that is revenue optimal in restricted settings. Finally, we study how squashing and reserve prices interact, and how equilibrium selection affects the revenue of GSP when features such as reserves or squashing are applied.

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“…These are algorithms that usually have worst-case exponential time, but may behave very well in practice or for special classes of games. This line of works originates with the celebrated Lemke-Howson algorithm (Lemke and Howson 1964), and for more recent works, see among others (Bhat and Leyton-Brown 2004;Thompson, Leung, and Leyton-Brown 2011) for the class of action-graph games and (Porter, Nudelman, and Shoham 2008) for the support enumeration method. More recently, there have also been experimental evaluations for methods that compute approximate equilibria, as reported in (Tsaknakis, Spirakis, and Kanoulas 2008;Kontogiannis and Spirakis 2011;Fearnley, Igwe, and Savani 2015), highlighting the need for creating new families of testbeds for such algorithms.…”

Section: Further Related Workmentioning

confidence: 99%

An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria

Fasoulakis

¹

,

Markakis

²

2019

AAAI

0

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We focus on the problem of computing approximate Nash equilibria in bimatrix games. In particular, we consider the notion of approximate well-supported equilibria, which is one of the standard approaches for approximating equilibria. It is already known that one can compute an ε-well-supported Nash equilibrium in time nO (log n/ε2), for any ε > 0, in games with n pure strategies per player. Such a running time is referred to as quasi-polynomial. Regarding faster algorithms, it has remained an open problem for many years if we can have better running times for small values of the approximation parameter, and it is only known that we can compute in polynomial-time a 0.6528-well-supported Nash equilibrium. In this paper, we investigate further this question and propose a much better quasi-polynomial time algorithm that computes a (1/2 + ε)-well-supported Nash equilibrium in time nO(log logn1/ε/ε2), for any ε > 0. Our algorithm is based on appropriately combining sampling arguments, support enumeration, and solutions to systems of linear inequalities.

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Computing Nash Equilibria of Action-Graph Games via Support Enumeration

Cited by 9 publications

References 17 publications

Revenue optimization in the generalized second-price auction

Revenue optimization in the generalized second-price auction

Revenue optimization in the generalized second-price auction

An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria

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