The complexity of fairness through equilibrium

Othman, Abraham; Papadimitriou, Christos H.; Rubinstein, Aviad

doi:10.1145/2600057.2602855

Cited by 26 publications

(27 citation statements)

References 18 publications

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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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“…Scarce resources, such as antique items or art collection pieces are even rarer -often unique (and thus indivisible). The problem of allocating discrete or indivisible resources is much more challenging because the theoretical guarantees from the divisible case do not always carry over; however, it can be tackled as well using market mechanisms [6,5,3,11]. In this paper, we are concerned with the question of allocating indivisible resources using the competitive equilibrium from equal incomes (CEEI).…”

Section: Introductionmentioning

confidence: 99%

Characterization and Computation of Equilibria for Indivisible Goods

Brânzei

Hosseini

Miltersen

2015

Algorithmic Game Theory

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We consider the problem of allocating indivisible goods in a way that is fair, using one of the leading market mechanisms in economics: the competitive equilibrium from equal incomes, which can be interpreted as a notion of fairness. Focusing on two major classes of valuations, namely perfect substitutes and perfect complements, we establish the computational properties of algorithms operating in this framework. For the class of valuations with perfect complements, our algorithm yields a surprisingly succinct characterization of instances that admit a competitive equilibrium from equal incomes.

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“…[BGHM16] showed PPAD-hardness of finding market equilibria with budget-capped utilities (this is proved using a variation on the piecewise-linear utilities proof of [CT09]). In the case of indivisible goods, [OPR16] showed that finding an approximate market equilibrium is hard, even one which is guaranteed to exist [Bud11].…”

Section: Additional Related Workmentioning

confidence: 99%

The Complexity of Pacing for Second-Price Auctions

Chen

Kroer

Kumar

2021

Preprint

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Budget constraints are ubiquitous in online advertisement auctions. To manage these constraints and smooth out the expenditure across auctions, the bidders (or the platform on behalf of them) often employ pacing: each bidder is assigned a multiplier between 0 and 1, and her bid on each item is multiplicatively scaled down by the multiplier. This naturally gives rise to a game in which each bidder strategically selects a multiplier. The appropriate notion of equilibrium in this game is the pacing equilibrium.In this work, we show that the problem of finding an approximate pacing equilibrium is PPAD-complete for second-price auctions. This resolves an open question of [CKSSM17]. As a consequence of our hardness result, we show that the tatonnement-style budget-management dynamics introduced by [BCI + 07] is unlikely to converge efficiently for repeated second-price auctions. Our hardness result also implies the existence of a refinement of supply-aware market equilibria which is hard to compute with simple linear utilities.

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The complexity of fairness through equilibrium

Cited by 26 publications

References 18 publications

Public Goods Games in Directed Networks

Public Goods Games in Directed Networks

Characterization and Computation of Equilibria for Indivisible Goods

The Complexity of Pacing for Second-Price Auctions

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