menu size complexity and revenue continuity of buy many
play

MENU-SIZE COMPLEXITY AND REVENUE CONTINUITY OF BUY-MANY MECHANISMS - PowerPoint PPT Presentation

Jan 03, 2024 β€’32 likes β€’72 views

MENU-SIZE COMPLEXITY AND REVENUE CONTINUITY OF BUY-MANY MECHANISMS Yi Yifen eng Ten eng University of Wisconsin-Madison Joint work with Shuchi Chawla and Christos Tzamos (UW-Madison) Buy-one mechanisms and buy-many mechanisms v(

  1. MENU-SIZE COMPLEXITY AND REVENUE CONTINUITY OF BUY-MANY MECHANISMS Yi Yifen eng Ten eng University of Wisconsin-Madison Joint work with Shuchi Chawla and Christos Tzamos (UW-Madison)

  2. Buy-one mechanisms and buy-many mechanisms v( )=$1000000 v( )=v( )=$1 1 $5 2 1 $2 3 $999 β–ͺ A seller has π‘œ heterogeneous items to sell to a single buyer. β–ͺ Typical buy-one mechanisms: buyer interact with the seller once. β–ͺ Optimal strategy: purchases the third menu option, pay $999. Buy-many mechanisms: buyer interact with the mechanism multiple times. β–ͺ Optimal strategy: repeatedly purchase , then repeatedly purchase , pay $16 in expectation. β–ͺ

  3. Menu-size complexity for near-optimal revenue β–ͺ How many menu options are needed for (1 βˆ’ πœ—) -approx in revenue? Buy- one mechanisms: infinite [Hart Nisan’13]. β–ͺ β–ͺ Buy-many mechanisms: finite. Theorem 1. For any distribution 𝐸 and πœ— ∈ [0,1] , exists mechanism 𝑁 with finite menu size 𝑔(π‘œ, πœ—) , such that 𝑆𝑓𝑀 𝐸 𝑁 β‰₯ 1 βˆ’ πœ— πΆπ‘£π‘§π‘π‘π‘œπ‘§π‘†π‘“π‘€ 𝐸 . 𝑔 π‘œ, πœ— = 1/πœ— 2 𝑃(π‘œ) . β–ͺ β–ͺ The doubly-exponential dependency of n is tight. Theorem 2. There exists 𝐸 being a distribution over XOS functions, such that for any mechanism 𝑁 with description complexity 2 2 𝑝(π‘œ1/4) , πΆπ‘£π‘§π‘π‘π‘œπ‘§π‘†π‘“π‘€ 𝐸 β‰₯ 𝑝 log π‘œ 𝑆𝑓𝑀 𝐸 𝑁 .

  4. Revenue Continuity When the buyer’s values for the sets of items perturb multiplicatively slightly, how much does the β–ͺ revenue change? Any 𝑀 ∼ 𝐸 is perturbed to 𝑀 β€² ∼ 𝐸′ , such that 𝑀 β€² 𝑇 ∈ β–ͺ 1 βˆ’ πœ— 𝑀(𝑇), 1 + πœ— 𝑀(𝑇) , βˆ€π‘‡ βŠ† [π‘œ] . Buy-one mechanisms: revenue may change significantly [Psomas et al.’19]. β–ͺ β–ͺ Continuity only holds for weaker additive perturbation [Rubinstein Weinberg’15] [ Brustle et al.’20]. β–ͺ Buy-many mechanisms: revenue changes slightly. Theorem 3. For any value distribution 𝐸 and any 1 Β± πœ— multiplicative perturbation 𝐸′ , πΆπ‘£π‘§π‘π‘π‘œπ‘§π‘†π‘“π‘€ 𝐸′ β‰₯ 1 βˆ’ π‘žπ‘π‘šπ‘§ π‘œ, πœ— πΆπ‘£π‘§π‘π‘π‘œπ‘§π‘†π‘“π‘€ 𝐸 . β–ͺ Note: such dependency on π‘œ is necessary. Theorem 4. There exists 𝐸 over unit-demand functions and a 1 Β± πœ— multiplicative perturbation 𝐸′ , such that πΆπ‘£π‘§π‘π‘π‘œπ‘§π‘†π‘“π‘€ 𝐸′ ≀ 1 πœ—π‘œ πΆπ‘£π‘§π‘π‘π‘œπ‘§π‘†π‘“π‘€ 𝐸 . β–ͺ Full paper: https://arxiv.org/abs/2003.10636

Recommend

Application of EventFlow to Model the Complexity and Continuity of Antipsychotic Use Among Youth

Application of EventFlow to Model the Complexity and Continuity of Antipsychotic Use Among Youth

Application of EventFlow to Model the Complexity and Continuity of Antipsychotic Use Among Youth Susan dosReis, 1 Wendy Camelo Castillo, 1 James Gardner, 1 Ming-Hui Tai, 1,2 1 Department of Pharmaceutical Health Services Research, University of

275 views β€’ 14 slides
CDM Program Size Complexity Klaus Sutner Carnegie Mellon University kolmogorov 2018/2/8 22:58

CDM Program Size Complexity Klaus Sutner Carnegie Mellon University kolmogorov 2018/2/8 22:58

CDM Program Size Complexity Klaus Sutner Carnegie Mellon University kolmogorov 2018/2/8 22:58 Wolfram Prize 1 Program-Size Complexity Prefix Complexity Incompleteness Small Universal 3 A Prize Question 4 In May 2007,

1.14k views β€’ 89 slides
Basics of Complexity Complexity = resources time space ink gates energy

Basics of Complexity Complexity = resources time space ink gates energy

Basics of Complexity Complexity = resources time space ink gates energy Complexity is a function Complexity = f (input size) Value depends on: problem encoding adj. list vs. adj matrix model of

326 views β€’ 17 slides
The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued

The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued

The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function Vassilis Gregoriades Technische Universit at Darmstadt, GERMANY A multi-valued (total) function from a set X to another set Y is a function

502 views β€’ 13 slides
Algorithmic Complexity Algorithmic Complexity "Algorithmic Complexity", also called

Algorithmic Complexity Algorithmic Complexity "Algorithmic Complexity", also called

Algorithmic Complexity Algorithmic Complexity "Algorithmic Complexity", also called "Running Time" or "Order of Growth", refers to the number of steps a program takes as a function of the size of its inputs. In

519 views β€’ 28 slides
CS 206 Data Structures Asymptotic Analysis 1 Complexity n How many resources will it take to

CS 206 Data Structures Asymptotic Analysis 1 Complexity n How many resources will it take to

CS 206 Data Structures Asymptotic Analysis 1 Complexity n How many resources will it take to solve a problem of a given size? q time q space n Expressed as a function of problem size (beyond some minimum size) q how do

649 views β€’ 33 slides
Breakfast Menu Breakfast Menu Paper: PopSet Fawn 120g Size: 594 x 420 mm Scale: 40%

Breakfast Menu Breakfast Menu Paper: PopSet Fawn 120g Size: 594 x 420 mm Scale: 40%

Breakfast Menu Breakfast Menu Paper: PopSet Fawn 120g Size: 594 x 420 mm Scale: 40% Breakfast Menu Paper: PopSet Fawn 120g Size: 594 x 420 mm Scale: 40% Breakfast Menu Page 4 Page 1 Page 2 Page 3

527 views β€’ 4 slides
Focus Slide . p.1 . p.2 CONTINUITY . p.2 CONTINUITY . p.2 CONTINUITY

Focus Slide . p.1 . p.2 CONTINUITY . p.2 CONTINUITY . p.2 CONTINUITY

Focus Slide . p.1 . p.2 CONTINUITY . p.2 CONTINUITY . p.2 CONTINUITY IN SOFTWARE SYSTEMS . p.2 CONTINUITY IN SOFTWARE SYSTEMS Dick Hamlet Portland State University Portland, OR, USA .

790 views β€’ 49 slides
Parikhs theorem from the complexity viewpoint Dmitry Chistikov University of Warwick, United

Parikhs theorem from the complexity viewpoint Dmitry Chistikov University of Warwick, United

Parikhs theorem from the complexity viewpoint Dmitry Chistikov University of Warwick, United Kingdom YR-OWLS, 03 June 2020 State complexity Program size complexity of problem: the minimum size of program that solves the problem State

1.55k views β€’ 105 slides
Continuity Definition 1 (Continuity) . A function f is said to be continuous at c if lim x c f

Continuity Definition 1 (Continuity) . A function f is said to be continuous at c if lim x c f

Continuity Definition 1 (Continuity) . A function f is said to be continuous at c if lim x c f ( x ) = f ( c ) . Goemetrically, this corresponds to the absence of any breaks in the graph of f at c . When weve calculated limits, most of the

260 views β€’ 3 slides
Teaching Continuity Goals Focus your planning efforts Thinking inward rather than just

Teaching Continuity Goals Focus your planning efforts Thinking inward rather than just

Teaching Continuity Goals Focus your planning efforts Thinking inward rather than just externally about continuity Clarity to your roles and responsibilities in a continuity incident Build a culture of continuity Building

410 views β€’ 21 slides
Research Continuity Goals Focus your planning efforts Thinking inward rather than just

Research Continuity Goals Focus your planning efforts Thinking inward rather than just

Research Continuity Goals Focus your planning efforts Thinking inward rather than just externally about continuity Clarity to your roles and responsibilities in a continuity incident Build a culture of continuity Building

402 views β€’ 17 slides
Business Continuity Board of Directors August 26, 2013 Agenda Business Continuity

Business Continuity Board of Directors August 26, 2013 Agenda Business Continuity

Business Continuity Board of Directors August 26, 2013 Agenda Business Continuity Business Continuity Plan Example Scenarios 2 2 What is Business Continuity? Business Continuity is ensuring that daily operations

99 views β€’ 7 slides
A Size Scaling Approach for Mixed-Size Placement Kalliopi Tsota, Cheng-Kok Koh, and

A Size Scaling Approach for Mixed-Size Placement Kalliopi Tsota, Cheng-Kok Koh, and

A Size Scaling Approach for Mixed-Size Placement Kalliopi Tsota, Cheng-Kok Koh, and Venkataramanan Balakrishnan School of Electrical and Computer Engineering, Purdue University Challenges in Physical Design High complexity and

876 views β€’ 10 slides
Online Accounting Services LOG-IN PAGE Menu ALCHAVO.com MAIN PAGE Menu ALCHAVO.com MAIN PAGE

Online Accounting Services LOG-IN PAGE Menu ALCHAVO.com MAIN PAGE Menu ALCHAVO.com MAIN PAGE

Online Accounting Services LOG-IN PAGE Menu ALCHAVO.com MAIN PAGE Menu ALCHAVO.com MAIN PAGE Menu ALCHAVO.com MAIN PAGE Menu ALCHAVO.com MOBILE Menu Menu BANK SUMMARY Menu BANK OUTSTANDING ITEMS Menu BANK UNDEFINED

863 views β€’ 57 slides
1 2 3 4 5 For certain users, when selecting items in the Enterprise Menu, the Menu will be

1 2 3 4 5 For certain users, when selecting items in the Enterprise Menu, the Menu will be

1 2 3 4 5 For certain users, when selecting items in the Enterprise Menu, the Menu will be shrunk horizontally and text will only be viewable by using the scroll bar at the bottom of the page. 6 In the previous release users security

527 views β€’ 31 slides
Continuity Michael Freeze MAT 151 UNC Wilmington Summer 2013 1 / 10 Section 3.2 :: Continuity

Continuity Michael Freeze MAT 151 UNC Wilmington Summer 2013 1 / 10 Section 3.2 :: Continuity

Continuity Michael Freeze MAT 151 UNC Wilmington Summer 2013 1 / 10 Section 3.2 :: Continuity 2 / 10 Continuity at x = c A function f is continuous at x = c if the following three conditions are all satisfied: 1 f ( c ) is defined, 2 lim x

229 views β€’ 10 slides
Continuity Clinic : Augmenting Continuity Clinic the Longitudinal Experience Erik Stratman, MD Sept

Continuity Clinic : Augmenting Continuity Clinic the Longitudinal Experience Erik Stratman, MD Sept

Continuity Clinic : Augmenting Continuity Clinic the Longitudinal Experience Erik Stratman, MD Sept 15, 2012 Objectives Describe various models of continuity training: What worked, What didn't? Implement processes that can improve the

678 views β€’ 29 slides
Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013,

Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013,

Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013, Warsaw Andrew Drucker Kernel-Size Lower Bounds Part 2/3 Andrew Drucker Kernel-Size Lower Bounds Note These slides are a slightly revised version

803 views β€’ 51 slides
Mobile Menu & Ordering The easiest way to share your menu with anyone and collect orders

Mobile Menu & Ordering The easiest way to share your menu with anyone and collect orders

Mobile Menu & Ordering The easiest way to share your menu with anyone and collect orders from anywhere The Mobile Menu allows you to share your restaurant menu with all mobile devices through a link or by scanning a QR code. The more

420 views β€’ 10 slides
Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013,

Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013,

Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013, Warsaw Andrew Drucker Kernel-Size Lower Bounds Part 1/3 Andrew Drucker Kernel-Size Lower Bounds Note These slides are taken (with minor

1.3k views β€’ 95 slides
Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013,

Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013,

Kernel-Size Lower Bounds: The Evidence from Complexity Theory Andrew Drucker IAS Worker 2013, Warsaw Andrew Drucker Kernel-Size Lower Bounds Part 3/3 Andrew Drucker Kernel-Size Lower Bounds Note These slides are taken (with minor

1.04k views β€’ 88 slides
Continuity Definition (Continuity) A function f is said to be continuous at c if lim x c f ( x

Continuity Definition (Continuity) A function f is said to be continuous at c if lim x c f ( x

Continuity Definition (Continuity) A function f is said to be continuous at c if lim x c f ( x ) = f ( c ). Alan H. SteinUniversity of Connecticut Continuity Definition (Continuity) A function f is said to be continuous at c if lim x c f

615 views β€’ 49 slides
Cayley Complexity of One Degree of Freedom Linkages in 2D Meera Sitharam Menghan Wang Heping

Cayley Complexity of One Degree of Freedom Linkages in 2D Meera Sitharam Menghan Wang Heping

Characterizing QS Cayley complexity Cayley Size & Computational Complexity Summary Cayley Complexity of One Degree of Freedom Linkages in 2D Meera Sitharam Menghan Wang Heping Gao University of Florida Department of Computer Information

683 views β€’ 53 slides

More recommend