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.

A closed-form upper-bound for the distribution of the weighted sum of rayleigh variates

2005 ◽  
Vol 9 (7) ◽  
pp. 589-591 ◽  
Author(s):  
G.K. Karagiannidis ◽  
T.A. Tsiftsis ◽  
N.C. Sagias
Keyword(s):  
Closed Form ◽  
Upper Bound ◽  
Weighted Sum

scholarly journals Reacting to outbreaks at neighboring localities

2020 ◽  
Author(s):  
Ceyhun Eksin ◽  
Martial-Ndeffo Mbah ◽  
Joshua S. Weitz
Keyword(s):  
Lower Bound ◽  
Behavior Change ◽  
Upper Bound ◽  
High Mobility ◽  
Cumulative Number ◽  
Weighted Sum ◽  
Combined Effects ◽  
Critical Levels ◽  
Metapopulation Model ◽  
Outbreak Size

AbstractWe study the dynamics of epidemics in a networked metapopulation model. In each subpopulation, representing a locality, disease propagates according to a modified susceptible-exposed-infected-recovered (SEIR) dynamics. We assume that individuals reduce their number of contacts as a function of the weighted sum of cumulative number of cases within the locality and in neighboring localities. We also assume that susceptible and exposed (pre-symptomatic and infectious) individuals can travel between localities. To investigate the combined effects of mobility and contact reduction on disease progression within interconnected localities, we consider a scenario with two localities where disease originates in one and is exported to the neighboring locality via travel of undetected pre-symptomatic individuals. We establish a lower bound on the outbreak size at the origin as a function of the speed of spread. We associate the behavior change at the disease-importing locality due to the outbreak size at the origin with the level of preparedness of the locality. Using the lower bound on the outbreak size at the origin, we establish an upper bound on the outbreak size at the importing locality as a function of the speed of spread and the level of preparedness for low mobility regimes. We show the accuracy of the bounds in determining critical levels of preparedness that stop the disease from becoming endemic at neighboring localities. Finally, we show how the benefit of preparedness diminishes under high mobility rates. Our results highlight the importance of preparedness at localities where cases are beginning to rise, and demonstrate the benefits of increase in contact reduction by considering the outbreaks in neighboring localities with severe, rather than weak, outbreaks.

On Riesz means of the coefficients of the Rankin–Selberg series

1999 ◽  
Vol 127 (1) ◽  
pp. 117-131 ◽  
Author(s):  
ALEKSANDAR IVIĆ ◽  
KOHJI MATSUMOTO ◽  
YOSHIO TANIGAWA
Keyword(s):  
Asymptotic Formula ◽  
Upper Bound ◽  
Error Term ◽  
Weighted Sum ◽  
Mean Square ◽  
Riesz Means ◽  
The Mean ◽  
Voronoi Formula

We study Δ(x; ϕ), the error term in the asymptotic formula for [sum ]n[les ]xcn, where the cns are generated by the Rankin–Selberg series. Our main tools are Voronoï-type formulae. First we reduce the evaluation of Δ(x; ϕ) to that of Δ1(x; ϕ), the error term of the weighted sum [sum ]n[les ]x(x−n)cn. Then we prove an upper bound and a sharp mean square formula for Δ1(x; ϕ), by applying the Voronoï formula of Meurman's type. We also prove that an improvement of the error term in the mean square formula would imply an improvement of the upper bound of Δ(x; ϕ). Some other related topics are also discussed.

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.

scholarly journals Equity-based incentive to coordinate shareholder-manager interests under information asymmetry

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhiping Zhou ◽  
Yao Yin ◽  
Mi Zhou ◽  
Hao Cheng ◽  
Panos M. Pardalos
Keyword(s):  
Information Asymmetry ◽  
Private Information ◽  
Comparative Statics ◽  
Theoretic Model ◽  
Business Operation ◽  
Hierarchical Levels ◽  
Research Findings ◽  
Expected Revenue ◽  
Perceived Unfairness ◽  
High Effort

<p style='text-indent:20px;'>The shareholder's interest oriented from business operation relies on opportunism regulation of the manager under asymmetry. Effective motivation incentives should be exploited to facilitate the manager's effort devotion enthusiasms. This paper establishes a theoretic model in which the shareholder offers equity-based incentive to a fairness-preferred manager to coordinate their interest conflicts and maximize her expected revenue. The manager exerts unverifiable levels of efforts toward both decision and coordination tasks making the most of his private information about fairness preference. Two interrelated performance measures on different hierarchical levels are considered for contracting purposes. In each situation, we derive the equilibrium effort choices and incentive coefficients of both participants, and investigate how these decisions are affected by fairness preference. Research findings suggest that the incorporation of firm equity dominates pure profit incentive in eliciting high effort levels toward two distinctive managerial tasks. Besides, the equity-based incentive weakens the perceived unfairness and facilitates the participants' expected revenue. Comparative statics and numerical analysis are conducted to demonstrate our results and the effectiveness of the proposed equity-based incentive. Finally, we summarize the contributions of this paper and put forward directions for further study.</p>

scholarly journals Bayes-Nash Equilibrium of the Generalized First-Price Auction

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaohu Han ◽  
Shulin Liu
Keyword(s):  
Nash Equilibrium ◽  
Incomplete Information ◽  
Explicit Expression ◽  
Search Engine ◽  
Reserve Price ◽  
Price Auction ◽  
Expected Revenue ◽  
The Difference ◽  
Optimal Reserve

We analyze the generalized first-price auction under incomplete information setting. Without setting a reserve price, the efficient symmetrical Bayes-Nash equilibrium is characterized and found to be increasing as the number of bidders is sufficiently large. Then, the explicit expression for the expected revenue of the search engine is found and the effect of the click rates of all the positions on the expected revenue is obtained. Finally, with setting of the reserve price, we have found the optimal reserve price and examine how the difference of the search engine’s revenues with setting reserve price and without setting reserve price varies with the reserve price.

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 Two methods for determining properly effcient solutions with a minimum upper bound for trade-offs

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1551-1559
Author(s):  
Behnam Hozzar ◽  
Ghasem Tohidi ◽  
Behrouz Daneshian
Keyword(s):  
Multiobjective Optimization ◽  
Nonlinear Optimization ◽  
Upper Bound ◽  
Optimization Problems ◽  
Ideal Point ◽  
Weighted Sum ◽  
Objective Functions ◽  
Trade Offs ◽  
The Ideal

This paper aims to investigate proper effciency in multiobjective optimization. We suggest two nonlinear optimization problems to determine upper bound for trade-offs among objective functions. Based on these problems we introduce some properly effcient solutions which are closer to the ideal point. Weighted sum scalarization and Kuhn-Tucker conditions will be used to obtain these nonlinear optimization problems.

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