Channel Auctions

2020 ◽  
Vol 66 (5) ◽  
pp. 2075-2082
Author(s):  
Eduardo M. Azevedo ◽  
David M. Pennock ◽  
Bo Waggoner ◽  
E. Glen Weyl
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Information Acquisition ◽  
Business Strategy ◽  
Equilibrium Price ◽  
Online Auction ◽  
English Auction ◽  
Dutch Auction ◽  
Auction Formats ◽  
Over Time

Standard auction formats feature either an upper bound on the equilibrium price that descends over time (as in the Dutch auction) or a lower bound on the equilibrium price that ascends over time (as in the English auction). We show that in some settings with costly information acquisition, auctions featuring both (viz., a narrowing channel of prices) outperform the standard formats. This Channel auction preserves some of benefits of both the English (truthful revelation) and Dutch (security for necessary information acquisition) auctions. Natural applications include housing, online auction sites like eBay, recording transactions on blockchains, and spectrum rights. This paper was accepted by Joshua Gans, business strategy.

No Time Limit and Time Limit Model of Multiple Round Dutch Auction Based on Genetic Network Programming

2011 ◽  
Vol 15 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Shingo Mabu ◽  
◽  
Donggeng Yu ◽  
Chuan Yue ◽  
Kotaro Hirasawa
Keyword(s):  
Genetic Network ◽  
Time Limit ◽  
Online Auction ◽  
Network Programming ◽  
English Auction ◽  
Auction Models ◽  
Limit Model ◽  
Dutch Auction ◽  
Multiple Round ◽  
Genetic Network Programming

Nowadays, Dutch auction is used widely at online auction sites. To make online Dutch auction more efficient and more intelligent, it is useful to develop an agent using evolutionary computation which will be adaptive to different auction environments. In this paper, a Genetic Network Programming (GNP) based strategy for auction agents has been proposed to do auctions in multiple round Dutch Auction environments under two types of auction models, no time limit model and time limit model. GNP is a graph-based evolutionary method extended from Genetic Algorithms (GA) and Genetic Programming (GP), which can create optimal solutions by evolution. Although the application of GNP to English auction has been done already, here, a new GNP structure is used for Dutch auction. The simulation results show that the GNP based strategy can also make the agents work well in Dutch auction and the advanced GNP structure makes the agents perform better than that in English auction.

scholarly journals Dynamic Fair Division Problem with General Valuations

2018 ◽  
Author(s):  
Bo Li ◽  
Wenyang Li ◽  
Yingkai Li
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Fair Division ◽  
Division Problem ◽  
Logarithmic Factor ◽  
Dynamic Algorithms ◽  
Dynamic Setting ◽  
Over Time

In this paper, we focus on how to dynamically allocate a divisible resource fairly among n players who arrive and depart over time. The players may have general heterogeneous valuations over the resource. It is known that the exact envy-free and proportional allocations may not exist in the dynamic setting [Walsh, 2011]. Thus, we will study to what extent we can guarantee the fairness in the dynamic setting. We first design two algorithms which are O(log n)-proportional and O(n)-envy-free for the setting with general valuations, and by constructing the adversary instances such that all dynamic algorithms must be at least Omega(1)-proportional and Omega(n/log n)-envy-free, we show that the bounds are tight up to a logarithmic factor. Moreover, we introduce the setting where the players' valuations are uniform on the resource but with different demands, which generalize the setting of [Friedman et al., 2015]. We prove an O(log n) upper bound and a tight lower bound for this case. 

scholarly journals Multiple closed orbits for N-body-type problems

1998 ◽  
Vol 58 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Shiqing Zhang
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Upper Bound ◽  
Critical Value ◽  
Body Type ◽  
Fixed Energy ◽  
Closed Orbits

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Isolated minima of the product of n linear forms

1953 ◽  
Vol 49 (1) ◽  
pp. 59-62 ◽  
Author(s):  
E. S. Barnes
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Linear Forms ◽  
Image Position

Letbe n linear forms with real coefficients and determinant Δ = ∥ aij∥ ≠ 0; and denote by M(X) the lower bound of | X1X2 … Xn| over all integer sets (u) ≠ (0). It is well known that γn, the upper bound of M(X)/|Δ| over all sets of forms Xi, is finite, and the value of γn has been determined when n = 2 and n = 3.

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

scholarly journals Encoding Two-Dimensional Range Top-k Queries

Algorithmica ◽  
2021 ◽  
Author(s):  
Seungbum Jo ◽  
Rahul Lingala ◽  
Srinivasa Rao Satti
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Total Order ◽  
Two Dimensional ◽  
Information Theoretic ◽  
Cartesian Tree ◽  
Dimensional Range

AbstractWe consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering $${\text{Top-}}{k}$$ Top- k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For an $$m \times n$$ m × n array, with $$m \le n$$ m ≤ n , we first propose an encoding for answering 1-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, whose query range is restricted to $$[1 \dots m][1 \dots a]$$ [ 1 ⋯ m ] [ 1 ⋯ a ] , for $$1 \le a \le n$$ 1 ≤ a ≤ n . Next, we propose an encoding for answering for the general (4-sided) $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries that takes $$(m\lg {{(k+1)n \atopwithdelims ()n}}+2nm(m-1)+o(n))$$ ( m lg ( k + 1 ) n n + 2 n m ( m - 1 ) + o ( n ) ) bits, which generalizes the joint Cartesian tree of Golin et al. [TCS 2016]. Compared with trivial $$O(nm\lg {n})$$ O ( n m lg n ) -bit encoding, our encoding takes less space when $$m = o(\lg {n})$$ m = o ( lg n ) . In addition to the upper bound results for the encodings, we also give lower bounds on encodings for answering 1 and 4-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, which show that our upper bound results are almost optimal.

scholarly journals Cheating in online auction – Towards explaining the popularity of English auction

2007 ◽  
Vol 6 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Mamata Jenamani ◽  
Yuhui Zhong ◽  
Bharat Bhargava
Keyword(s):  
Online Auction ◽  
English Auction

On the Modal μ-Calculus Over Finite Symmetric Graphs

2015 ◽  
Vol 65 (4) ◽  
Author(s):  
Giovanna D’Agostino ◽  
Giacomo Lenzi
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Satisfiability Problem ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Symmetric Graphs ◽  
Trivial Consequence

AbstractIn this paper we consider the alternation hierarchy of the modal μ-calculus over finite symmetric graphs and show that in this class the hierarchy is infinite. The μ-calculus over the symmetric class does not enjoy the finite model property, hence this result is not a trivial consequence of the strictness of the hierarchy over symmetric graphs. We also find a lower bound and an upper bound for the satisfiability problem of the μ-calculus over finite symmetric graphs.

Information Acquisition as Business Strategy

1992 ◽  
Vol 58 (3) ◽  
pp. 750 ◽  
Author(s):  
Chun-Hao Chang ◽  
Chi-Wen Jevons Lee
Keyword(s):  
Information Acquisition ◽  
Business Strategy
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