Why Prices Need Algorithms

Roughgarden, Tim; Talgam-Cohen, Inbal

doi:10.1145/2764468.2764515

Cited by 22 publications

(27 citation statements)

References 32 publications

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“…Using complexity theoretic certi cates, [36] obtained a similar result indicating that for graphical valuations that only exhibit complementarity a pricing equilibrium with anonymous graphical pricing does not exist. Example 3.13 indicates that eorem 3.7 can also be used to recover this result.…”

Section: Nonexistence Examplesmentioning

confidence: 89%

“…us, roughly speaking, series-parallel networks represent se ings where conditional on assignment of some items to agents, the valuations additively decompose over smaller bundles. • It was noted in [36] that it is "rare" to nd a class of valuations V which does not admit a Walrasian equilibrium, yet admits a pricing equilibrium that relies on a pricing rule P that can be expressed strictly more succinctly than the valuations themselves. eorem 3.7 o ers an explanation as to why this might be the case for graphical valuations (and anonymous graphical pricing).…”

Section: Remarksmentioning

confidence: 99%

“…In a recent paper, [36] identify a surprising connection between the existence of a pricing equilibrium and the computational complexity of welfare-maximization, nding demanded bundles, and identifying revenue-maximizing allocations for a seller. eir results suggest that if the welfaremaximization problem is computationally strictly harder than the problem of nding demanded bundles (under anonymous item-pricing) then a Walrasian equilibrium does not exist.…”

Section: Introductionmentioning

confidence: 99%

“…ese results provide complexity theoretic certi cates that can be used for testing the existence of a pricing equilibrium. Using such certi cates [36] identify new subclasses of valuations (e.g., pair-demand valuations, triplet valuations, and positive graphical valuations), where a pricing equilibrium with anonymous graphical pricing does not exist, thereby complementing the results of this paper as well as [13]. We emphasize that in the current paper, we provide an interesting equivalence between Walrasian equilibrium existence and the existence of a pricing equilibrium with anonymous graphical pricing for simple graphical valuations, through a novel connection to the partitioning polytope.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Equilibria and Graphical Valuations

Candogan

Ozdaglar

Parrilo

2018

ACM Trans. Econ. Comput.

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We study pricing equilibria for graphical valuations [1, 14] , which is a class of valuations that admit a compact representation. ese valuations are associated with a value graph, whose nodes correspond to items, and edges encode (pairwise) complementarities/substitutabilities between items. It is known that for graphical valuations a Walrasian equilibrium (a pricing equilibrium that relies on anonymous item prices) does not exist in general. On the other hand, a pricing equilibrium exists when the seller uses an agent-speci c graphical pricing rule that involves prices for each item and markups/discounts for pairs of items. We study the existence of pricing equilibria with simpler pricing rules which either (i) require anonymity (so that prices are identical for all agents) while allowing for pairwise markups/discounts, or (ii) involve o ering prices only for items. We show that a pricing equilibrium with the la er pricing rule exists if and only if a Walrasian equilibrium exists, whereas the former pricing rule may guarantee the existence of a pricing equilibrium even for graphical valuations that do not admit a Walrasian equilibrium. Interestingly, by exploiting a novel connection between the existence of a pricing equilibrium and the partitioning polytope associated with the underlying graph, we also establish that for simple (series-parallel) value graphs a pricing equilibrium with anonymous graphical pricing rule exists if and only if a Walrasian equilibrium exists. ese equivalence results imply that simpler pricing rules (i) and (ii) do not guarantee the existence of a pricing equilibrium for all graphical valuations.

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Section: Nonexistence Examplesmentioning

confidence: 89%

Section: Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pricing Equilibria and Graphical Valuations

Candogan

Ozdaglar

Parrilo

2018

ACM Trans. Econ. Comput.

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“…Moreover, budget-additive valuations are of interest in a variety of applications, most prominently in online advertising [39,38]. They have been studied frequently in the literature, e.g., for offline social welfare maximization [3,6,48,15,34], online algorithms [11,21], mechanism design [12], Walrasian equilibrium [46,28], and market equilibrium [8,17].…”

mentioning

confidence: 99%

Approximating the Nash Social Welfare with Budget-Additive Valuations

Garg¹,

Hoefer²,

Mehlhorn³

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every ε > 0, our algorithm obtains a (2.404 + ε)-approximation in time polynomial in the input size and 1/ε.Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties.Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [17]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest.

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Complexity-Theoretic Barriers in Economics

Roughgarden

2019

The Future of Economic Design

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Why Prices Need Algorithms

Cited by 22 publications

References 32 publications

Pricing Equilibria and Graphical Valuations

Pricing Equilibria and Graphical Valuations

Approximating the Nash Social Welfare with Budget-Additive Valuations

Complexity-Theoretic Barriers in Economics

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