On Optimal Auctions for Mixing Exclusive and Shared Matching in Platforms

2020 ◽  
Vol 66 (6) ◽  
pp. 2653-2676 ◽  
Author(s):  
Hemant K. Bhargava ◽  
Gergely Csapó ◽  
Rudolf Müller
Keyword(s):  
Private Information ◽  
Mathematical Program ◽  
Upper Bounds ◽  
One Dimension ◽  
Reserve Price ◽  
Computational Burden ◽  
Incentive Compatible ◽  
Optimal Auction ◽  
Auction Format ◽  
Exclusive Or

Platforms create value by matching participants on alternate sides of the marketplace. Although many platforms practice one-to-one matching (e.g., Uber), others can conduct and monetize one-to-many simultaneous matches (e.g., lead-marketing platforms). Both formats involve one dimension of private information, a participant’s valuation for exclusive or shared allocation, respectively. This paper studies the problem of designing an auction format for platforms that mix the modes rather than limit to one and, therefore, involve both dimensions of information. We focus on incentive-compatible auctions (i.e., where truthful bidding is optimal) because of ease of participation and implementation. We formulate the problem to find the revenue-maximizing incentive-compatible auction as a mathematical program. Although hard to solve, the mathematical program leads to heuristic auction designs that are simple to implement, provide good revenue, and have speedy performance, all critical in practice. It also enables creation of upper bounds on the (unknown) optimal auction revenue, which are useful benchmarks for our proposed auction designs. By demonstrating a tight gap for our proposed two-dimensional reserve-price-based mechanism, we prove that it has excellent revenue performance and places low information and computational burden on the platform and participants. This paper was accepted by Chris Forman, information systems.

scholarly journals Budget Feasible Mechanisms on Matroids

Algorithmica ◽  
2020 ◽  
Author(s):  
Stefano Leonardi ◽  
Gianpiero Monaco ◽  
Piotr Sankowski ◽  
Qiang Zhang
Keyword(s):  
Polynomial Time ◽  
Private Information ◽  
Independent Set ◽  
Deterministic Algorithm ◽  
Matroid Intersection ◽  
Practical Applications ◽  
Incentive Compatible ◽  
The Cost ◽  
Special Case ◽  
Budget Feasible

AbstractMotivated by many practical applications, in this paper we study budget feasible mechanisms with the goal of procuring an independent set of a matroid. More specifically, we are given a matroid $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) . Each element of the ground set E is controlled by a selfish agent and the cost of the element is private information of the agent itself. A budget limited buyer has additive valuations over the elements of E. The goal is to design an incentive compatible budget feasible mechanism which procures an independent set of the matroid of largest possible value. We also consider the more general case of the pair $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) satisfying only the hereditary property. This includes matroids as well as matroid intersection. We show that, given a polynomial time deterministic algorithm that returns an $$\alpha $$ α -approximation to the problem of finding a maximum-value independent set in $${\mathcal {M}}$$ M , there exists an individually rational, truthful and budget feasible mechanism which is $$(3\alpha +1)$$ ( 3 α + 1 ) -approximated and runs in polynomial time, thus yielding also a 4-approximation for the special case of matroids.

scholarly journals Revenue-Capped Efficient Auctions

2019 ◽  
Vol 18 (3) ◽  
pp. 1284-1320 ◽  
Author(s):  
Nozomu Muto ◽  
Yasuhiro Shirata ◽  
Takuro Yamashita
Keyword(s):  
Upper Bound ◽  
Private Information ◽  
Weighted Sum ◽  
Reserve Price ◽  
Total Surplus ◽  
Good For ◽  
Expected Revenue ◽  
Social Surplus

Abstract We study an auction that maximizes the expected social surplus under an upper-bound constraint on the seller’s expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when (i) the auction designer is “pro-buyer”, that is, he maximizes the weighted sum of the buyers’ and seller’s auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multiunit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, “bunching” is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least “at the top,” that is, “no distortion at the top” fails.

scholarly journals Efficiency, Welfare, and Political Competition *

2015 ◽  
Vol 131 (1) ◽  
pp. 461-518 ◽  
Author(s):  
Felix J. Bierbrauer ◽  
Pierre C. Boyer
Keyword(s):  
Private Information ◽  
Political Competition ◽  
Income Taxation ◽  
Symmetric Equilibrium ◽  
Public Goods Provision ◽  
Trade Off ◽  
Private Goods ◽  
Incentive Compatible ◽  
Equity And Efficiency ◽  
Pareto Efficient

Abstract We study political competition in an environment in which voters have private information about their preferences. Our framework covers models of income taxation, public-goods provision, or publicly provided private goods. Politicians are vote-share maximizers. They can propose any policy that is resource-feasible and incentive-compatible. They can also offer special favors to subsets of the electorate. We prove two main results. First, the unique symmetric equilibrium is such that policies are surplus-maximizing and hence first-best Pareto-efficient. Second, there is a surplus-maximizing policy that wins a majority against any welfare-maximizing policy. Thus, in our model, policies that trade off equity and efficiency considerations are politically infeasible.

scholarly journals Market Selection and the Information Content of Prices

Econometrica ◽  
2021 ◽  
Vol 89 (5) ◽  
pp. 2049-2079
Author(s):  
Alp E. Atakan ◽  
Mehmet Ekmekci
Keyword(s):  
Information Content ◽  
Private Information ◽  
Information Aggregation ◽  
Reserve Price ◽  
Market Selection ◽  
Uniform Price Auction ◽  
Uniform Price ◽  
Common Value ◽  
Common Value Auctions ◽  
Price Auction

We study information aggregation when n bidders choose, based on their private information, between two concurrent common‐value auctions. There are k s identical objects on sale through a uniform‐price auction in market s and there are an additional k r objects on auction in market r, which is identical to market s except for a positive reserve price. The reserve price in market r implies that information is not aggregated in this market. Moreover, if the object‐to‐bidder ratio in market s exceeds a certain cutoff, then information is not aggregated in market s either. Conversely, if the object‐to‐bidder ratio is less than this cutoff, then information is aggregated in market s as the market grows arbitrarily large. Our results demonstrate how frictions in one market can disrupt information aggregation in a linked, frictionless market because of the pattern of market selection by imperfectly informed bidders.

Discussion: “Limits to Voluntary Disclosure in Efficient Markets”

1996 ◽  
Vol 11 (3) ◽  
pp. 388-391 ◽  
Author(s):  
Rick Antle
Keyword(s):  
Capital Market ◽  
Private Information ◽  
Voluntary Disclosure ◽  
One Dimension ◽  
Efficient Markets ◽  
Voluntary Disclosures ◽  
Accounting Research ◽  
Coding Schemes

This paper addresses a very important and rich topic for accounting research: what are the incentives for making voluntary disclosures to an efficient capital market when private information has more than one dimension? There are many aspects to this topic, and I will use this discussion as a vehicle for discussing four of them. In particular, this discussion addresses aggregation, coding schemes, auditing, and sender-receiver models. Particular aspects of the paper are used to illustrate various points about these general ideas.

The Marriage Problem with Interdependent Preferences

2020 ◽  
Vol 22 (02) ◽  
pp. 2040005
Author(s):  
Mohsen Pourpouneh ◽  
Rasoul Ramezanian ◽  
Arunava Sen
Keyword(s):  
Private Information ◽  
Common Knowledge ◽  
Priority Rules ◽  
Marriage Problem ◽  
Interdependent Preferences ◽  
Incentive Compatible ◽  
Ex Post ◽  
Women’S Preferences ◽  
Matching Rules

This paper considers the Gale–Shapley model with interdependent preferences. Women’s preferences over men are common knowledge but whether or not a man is acceptable depends on the preferences of men which are private information. It is shown that no ex-post incentive-compatible and ex-post stable matching rules exist. A characterization of ex-post incentive-compatible, ex-post individually rational and ex-post nonbossy matching rules in terms of modified priority rules is provided.

scholarly journals Optimal auctions through deep learning

2021 ◽  
Vol 64 (8) ◽  
pp. 109-116
Author(s):  
Paul Dütting ◽  
Zhe Feng ◽  
Harikrishna Narasimhan ◽  
David C. Parkes ◽  
Sai S. Ravindranath
Keyword(s):  
Deep Learning ◽  
Learning Problem ◽  
Auction Design ◽  
Single Item ◽  
Optimal Auctions ◽  
Incentive Compatible ◽  
Optimal Mechanism ◽  
Optimal Auction ◽  
Constrained Learning ◽  
High Degree

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30--40 years of intense research, the problem remains unsolved for settings with two or more items. We overview recent research results that show how tools from deep learning are shaping up to become a powerful tool for the automated design of near-optimal auctions auctions. In this approach, an auction is modeled as a multilayer neural network, with optimal auction design framed as a constrained learning problem that can be addressed with standard machine learning pipelines. Through this approach, it is possible to recover to a high degree of accuracy essentially all known analytically derived solutions for multi-item settings and obtain novel mechanisms for settings in which the optimal mechanism is unknown.

scholarly journals Incentive-Compatible Classification

2020 ◽  
Vol 34 (05) ◽  
pp. 7055-7062
Author(s):  
Yakov Babichenko ◽  
Oren Dean ◽  
Moshe Tennenholtz
Keyword(s):  
Single Agent ◽  
Classification Problem ◽  
Upper Bounds ◽  
The Other ◽  
Worst Case ◽  
Incentive Compatible ◽  
Natural Mechanism ◽  
Strategy Proof ◽  
The Ideal

We investigate the possibility of an incentive-compatible (IC, a.k.a. strategy-proof) mechanism for the classification of agents in a network according to their reviews of each other. In the α-classification problem we are interested in selecting the top α fraction of users. We give upper bounds (impossibilities) and lower bounds (mechanisms) on the worst-case coincidence between the classification of an IC mechanism and the ideal α-classification.We prove bounds which depend on α and on the maximal number of reviews given by a single agent, Δ. Our results show that it is harder to find a good mechanism when α is smaller and Δ is larger. In particular, if Δ is unbounded, then the best mechanism is trivial (that is, it does not take into account the reviews). On the other hand, when Δ is sublinear in the number of agents, we give a simple, natural mechanism, with a coincidence ratio of α.

A Path Based Algorithm for Solve the Hazardous Materials Transportation Bilevel Problem

2012 ◽  
Vol 253-255 ◽  
pp. 1082-1088
Author(s):  
José Fernando Camacho Vallejo ◽  
Rafael Muñoz Sánchez
Keyword(s):  
Mathematical Program ◽  
Transportation Network ◽  
Shortest Paths ◽  
Hazardous Materials ◽  
Upper Bounds ◽  
Government Agency ◽  
Population Exposure ◽  
Hazardous Materials Transportation ◽  
Total Cost ◽  
Upper Level

In this work we consider the problem of determining a set of optimal tolls on the arcs of a multicommodity transportation network. The problem is formulated as a bilevel mathematical program where the upper level consists in a government agency that regulate the traffic of the dangerous materials by imposing tolls on arcs of the network trying to minimize the risk for the population in the case when an accident occurs to the carriers, while the lower level is represented by a group of carriers traveling on shortest paths with respect to a generalized travel cost. So, the problem can be seen in a simplistic form as find the equilibrium between tolls that minimize the population exposure to the risk and tolls that are convenient for the shippers. The paper applies a path based algorithm to solve a bi-level multi-commodity optimal toll setting ‘hazmat’ problem. The algorithm consists in find upper bounds for the tolls considering the total cost and the risk associated to a particular path. We made several experiments and the results are shown in this work.

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