On the Complexity of Equilibrium Computation in First-Price Auctions

Filos-Ratsikas, Aris; Giannakopoulos, Yiannis; Hollender, Alexandros; Lazos, Philip; Poças, Diogo

doi:10.1145/3465456.3467627

Cited by 13 publications

(3 citation statements)

References 62 publications

(114 reference statements)

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“…The PPAD-completeness of Nash equilibria was established in [11,18] and extended recently in [36,37]. Over the past decades, a broad range of problems have been proved to be PPAD-hard, including equilibrium computation [1,12,16,21], market equilibrium [9,10,14,15,43], equilibrium in auction [13,25], fair allocation [33], min-max optimization [22] and problems in financial networks [39].…”

Section: Related Workmentioning

confidence: 99%

Public Goods Games in Directed Networks

Papadimitriou

Peng

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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Public goods games in undirected networks are generally known to have pure Nash equilibria, which are easy to find. In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems: The existence of pure Nash equilibria is NP-hard to decide, and mixed Nash equilibria are PPAD-hard to find. We define general utility public goods games, and prove a complexity dichotomy result for finding pure equilibria, and a PPAD-completeness proof for mixed Nash equilibria. Even in the divisible goods variant of the problem, where existence is easy to prove, finding the equilibrium is PPAD-complete. Finally, when the treewidth of the directed network is appropriately bounded, we prove that polynomial-time algorithms are possible.CCS Concepts: • Theory of computation → Algorithmic game theory; Exact and approximate computation of equilibria; Network games.

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Section: Related Workmentioning

confidence: 99%

Public Goods Games in Directed Networks

Papadimitriou

Peng

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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“…Fixed point computation. Besides the applications above, the class FIXP also captures the complexity of other problems, such as branching process and context-free grammars [Etessami and Yannakakis, 2010], equilibrium refinements [Etessami et al, 2014;Etessami, 2021], and more recently the complexity of computing a Bayes-Nash equilibrium in the first-price auction with subjective priors [Filos-Ratsikas et al, 2021]. Besides FIXP, there are some other computational classes that capture the complexity of different fixed point problems, namely the classes BU [Deligkas et al, 2021] and BBU [Batziou et al, 2021] which correspond to the Borsuk-Ulam theorem [Borsuk, 1933], and the class HB [Goldberg and Hollender, 2021], which corresponds to the Hairy Ball theorem [Poincaré, 1885].…”

Section: Related Workmentioning

confidence: 99%

FIXP-Membership via Convex Optimization: Games, Cakes, and Markets

et al. 2023

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We introduce a new technique for proving membership of problems in FIXP -the class capturing the complexity of computing a fixed-point of an algebraic circuit. Our technique constructs a "pseudogate" which can be used as a black box when building FIXP circuits. This pseudogate, which we term the "OPT-gate", can solve most convex optimization problems. Using the OPT-gate, we prove new FIXP-membership results, and we generalize and simplify several known results from the literature on fair division, game theory and competitive markets.In particular, we prove complexity results for two classic problems: computing a market equilibrium in the Arrow-Debreu model with general concave utilities is in FIXP, and computing an envy-free division of a cake with very general valuations is FIXP-complete. We further showcase the wide applicability of our technique, by using it to obtain simplified proofs and extensions of known FIXP-membership results for equilibrium computation for various types of strategic games, as well as the pseudomarket mechanism of Hylland and Zeckhauser.

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“…For details, we refer to Roughgarden [41, chapter 20]. 3 This version, together with some further simplifications, is used in subsequent work by Filos-Ratsikas et al [24] to prove that computing an approximate equilibrium of a first-price auction with subjective priors is PPAD-hard. 4 See http://www.nyu.edu/projects/adjustedwinner for a demonstration and implementation of the procedure.…”

Section: Appendix a Constant Number Of Agentsmentioning

confidence: 99%

Consensus Halving for Sets of Items

et al. 2022

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Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work shows that, when the resource is represented by an interval, a consensus halving with at most n cuts always exists but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting in which the resource consists of a set of items without a linear ordering. For agents with linear and additively separable utilities, we present a polynomial-time algorithm that computes a consensus halving with at most n cuts and show that n cuts are almost surely necessary when the agents’ utilities are randomly generated. On the other hand, we show that, for a simple class of monotonic utilities, the problem already becomes polynomial parity argument, directed version–hard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus k-splitting, with which we wish to divide the resource into k parts in possibly unequal ratios and provide some consequences of our results on the problem of computing small agreeable sets.

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On the Complexity of Equilibrium Computation in First-Price Auctions

Cited by 13 publications

References 62 publications

Public Goods Games in Directed Networks

Public Goods Games in Directed Networks

FIXP-Membership via Convex Optimization: Games, Cakes, and Markets

Consensus Halving for Sets of Items

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