A note on the efficiency of position mechanisms with budget constraints

Voudouris, Alexandros A.

doi:10.1016/j.ipl.2018.11.004

“…As an e ciency benchmark, liquid welfare has been studied recently in di erent contexts such as in the design of truthful mechanisms (see [Dobzinski and Paes Leme, 2014;Xiao, 2015, 2017]) and in the analysis of combinatorial Walrasian equilibria with budgets [Dughmi et al, 2016]. In the context of the price of anarchy, it was considered recently in simultaneous rst price auctions by Azar et al [2017] and in position auctions by Voudouris [2019]. Caragiannis and Voudouris [2016] were the rst to prove that the liquid price of anarchy of the Kelly mechanism is constant.…”

Section: Lpoamentioning

confidence: 99%

The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users

Caragiannis

¹

,

Voudouris

²

2021

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We study the efficiency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such a mechanism decides the fraction of the resource that each user will receive and a payment that will be collected from her. Users are self-interested and aim to maximize their utility (defined as their value for the resource fraction they receive minus their payment). Starting with the seminal work of Johari and Tsitsiklis, a long list of papers studied the price of anarchy (in terms of the social welfare—the total users’ value) of resource allocation mechanisms for a variety of allocation and payment rules. Here, we further assume that each user has a budget constraint that invalidates strategies that yield a payment that is higher than the user’s budget. This subtle assumption, which is arguably more realistic, constitutes the traditional price of anarchy analysis meaningless as the set of equilibria may change drastically and their social welfare can be arbitrarily far from optimal. Instead, we study the price of anarchy using the liquid welfare benchmark that measures efficiency taking budget constraints into account. We show a tight bound of 2 on the liquid price of anarchy of the well-known Kelly mechanism and prove that this result is essentially best possible among all multiuser resource allocation mechanisms. This comes in sharp contrast to the no-budget setting where there are mechanisms that considerably outperform Kelly in terms of social welfare and even achieve full efficiency. In our proofs, we exploit the particular structure of worst-case games and equilibria, which also allows us to design (nearly) optimal two-player mechanisms by solving simple differential equations.

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“…Following their work, Caragiannis and Voudouris [2018] characterized the structure of worst-case pure equilibria and proved tight bounds on the liquid price of anarchy for almost all divisible resource allocation mechanisms. In a similar spirit, Voudouris [2019] showed tight bounds on the pure liquid price of anarchy and stability for ad auctions, including the generalized second price auction and VCG. Our work is mostly related to that of Azar et al [2017] who showed a constant bound on the liquid price of anarchy of simultaneous first and second price auctions for Bayes-Nash equilibria when the agents have additive valuation functions, and a tight bound of 2 on the liquid price of anarchy for pure equilibria when the agents have fractionallysubadditive valuations.…”

Section: Introductionmentioning

confidence: 87%

Simple combinatorial auctions with budget constraints

Voudouris

¹

2020

Theoretical Computer Science

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We study the efficiency of simple combinatorial auctions for the allocation of a set of items to a set of agents, with private subadditive valuation functions and budget constraints. e class we consider includes all auctions that allocate each item independently to the agent that submits the highest bid for it, and requests a payment that depends on the bids of all agents only for this item. Two well-known examples of this class are the simultaneous first and second price auctions. We focus on the pure equilibria of the induced strategic games, and using the liquid welfare as our efficiency benchmark, we show an upper bound of 2 on the price of anarchy for any auction in this class, as well as a tight corresponding lower bound on the price of stability for all auctions whose payment rules are convex combinations of the bids.is implies a tight bound of 2 on the price of stability of the well-known simultaneous first and second price auctions, which are members of the class. Additionally, we show lower bounds for the whole class, for more complex auctions (like VCG), and for se ings where the budgets are assumed to be common knowledge rather than private information.

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“…Following their work, Caragiannis and Voudouris [2018] characterized the structure of worst-case pure equilibria and proved tight bounds on the liquid price of anarchy for almost all divisible resource allocation mechanisms. In a similar spirit, Voudouris [2019] showed tight bounds on the pure liquid price of anarchy and stability for ad auctions, including the generalized second price auction and VCG. Our work is mostly related to that of Azar et al [2017] who showed a constant bound on the liquid price of anarchy of simultaneous first and second price auctions for Bayes-Nash equilibria when the agents have additive valuation functions, and a tight bound of 2 on the liquid price of anarchy for pure equilibria when the agents have fractionallysubadditive valuations.…”

Section: Introductionmentioning

confidence: 87%

Simple combinatorial auctions with budget constraints

Voudouris

2020

Preprint

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0

View full text Add to dashboard Cite

We study the efficiency of simple combinatorial auctions for the allocation of a set of items to a set of agents, with private subadditive valuation functions and budget constraints. e class we consider includes all auctions that allocate each item independently to the agent that submits the highest bid for it, and requests a payment that depends on the bids of all agents only for this item. Two well-known examples of this class are the simultaneous first and second price auctions. We focus on the pure equilibria of the induced strategic games, and using the liquid welfare as our efficiency benchmark, we show an upper bound of 2 on the price of anarchy for any auction in this class, as well as a tight corresponding lower bound on the price of stability for all auctions whose payment rules are convex combinations of the bids.is implies a tight bound of 2 on the price of stability of the well-known simultaneous first and second price auctions, which are members of the class. Additionally, we show lower bounds for the whole class, for more complex auctions (like VCG), and for se ings where the budgets are assumed to be common knowledge rather than private information.

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A note on the efficiency of position mechanisms with budget constraints

Cited by 4 publications

References 25 publications

The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users

The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users

Simple combinatorial auctions with budget constraints

Simple combinatorial auctions with budget constraints

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