You are organizing a conference that has received n submitted papers. Your goal is to get people to review as many of them as possible. To do this, you have enlisted the help of k reviewers. Each reviewer i has a cost s;j for writing a review for paper j. The strategy of each reviewer i is to select a subset of papers to write a review for. They can select any subset S; C {1,2,...,n}, as long as the total cost to write all reviews is less than T (the time before the deadline): E Sij ST. jeS, Reviews are costly, so you want to reward them for their efforts. However, each paper and review has to be treated equally: specifically, there is a budget of 1 for each paper, that will be evenly shared across all reviewers who reviewed that paper. For example, if 4 reviewers reviewed a paper they will receive 1/4 each. If only one reviewer reviews the paper they will receive all the reward. Of course, each reviewer i wants to maximize their utility ui, which is the reward R; over all papers they receive minus the effort they put into writting reviews: ui = R; - Sij. jeS, You can assume that for the given si,'s, there is a combination of strategies S; where every reviewer has positive utility and all papers get at least one review. However, this outcome might not be a pure Nash equilibrium. As a designer, your goal is to find the fraction of papers that receive at least 1 review at a pure Nash equilibrium, for the worst possible combination of s;,'s satisfying the assumption. (a) Show that there exists a set of sij's such that the fraction of papers that receive reviews is close to 1/n. Given the previous negative result, you think about increasing the reward of each paper from 1 to B > 1. (b) Show that for B = 2 this fraction is close to 1/3. [Hint: You can consider an instance with 3n +1 papers and only n will be reviewed.]
You are organizing a conference that has received n submitted papers. Your goal is to get people to review as many of them as possible. To do this, you have enlisted the help of k reviewers. Each reviewer i has a cost s;j for writing a review for paper j. The strategy of each reviewer i is to select a subset of papers to write a review for. They can select any subset S; C {1,2,...,n}, as long as the total cost to write all reviews is less than T (the time before the deadline): E Sij ST. jeS, Reviews are costly, so you want to reward them for their efforts. However, each paper and review has to be treated equally: specifically, there is a budget of 1 for each paper, that will be evenly shared across all reviewers who reviewed that paper. For example, if 4 reviewers reviewed a paper they will receive 1/4 each. If only one reviewer reviews the paper they will receive all the reward. Of course, each reviewer i wants to maximize their utility ui, which is the reward R; over all papers they receive minus the effort they put into writting reviews: ui = R; - Sij. jeS, You can assume that for the given si,'s, there is a combination of strategies S; where every reviewer has positive utility and all papers get at least one review. However, this outcome might not be a pure Nash equilibrium. As a designer, your goal is to find the fraction of papers that receive at least 1 review at a pure Nash equilibrium, for the worst possible combination of s;,'s satisfying the assumption. (a) Show that there exists a set of sij's such that the fraction of papers that receive reviews is close to 1/n. Given the previous negative result, you think about increasing the reward of each paper from 1 to B > 1. (b) Show that for B = 2 this fraction is close to 1/3. [Hint: You can consider an instance with 3n +1 papers and only n will be reviewed.]
Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![You are organizing a conference that has received n submitted papers. Your goal is to get people to review as many
of them as possible. To do this, you have enlisted the help of k reviewers. Each reviewer i has a cost s;; for writing a
review for paper j. The strategy of each reviewer i is to select a subset of papers to write a review for. They can select
any subset S; C {1,2,...,n}, as long as the total cost to write all reviews is less than T (the time before the deadline):
E Sij <T.
jeS
Reviews are costly, so you want to reward them for their efforts. However, each paper and review has to be treated
equally: specifically, there is a budget of 1 for each paper, that will be evenly shared across all reviewers who reviewed
that
For example, if 4 reviewers reviewed a paper they will receive 1/4 each. If only one reviewer reviews
раper.
the paper they will receive all the reward. Of course, each reviewer i wants to maximize their utility u;, which is the
reward R; over all papers they receive minus the effort they put into writting reviews:
U; = R; – Sij.
jeSi
You can assume that for the given s;;'s, there is a combination of strategies S; where every reviewer has positive
utility and all papers get at least one review. However, this outcome might not be a pure Nash equilibrium. As a
designer, your goal is to find the fraction of papers that receive at least 1 review at a pure Nash equilibrium, for the
worst possible combination of s;,'s satisfying the assumption.
(a) Show that there exists a set of sij's such that the fraction of papers that receive reviews is close to 1/n.
Given the previous negative result, you think about increasing the reward of each paper from 1 to B > 1.
(b) Show that for B = 2 this fraction is close to 1/3. [Hint: You can consider an instance with 3n + 1
only n will be reviewed.]
раpers
and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3592dcf-4763-401e-a3ff-d77a4658cc9e%2F12dd5a05-9237-4d10-b5b4-5ead24e92188%2Fn8qshgf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You are organizing a conference that has received n submitted papers. Your goal is to get people to review as many
of them as possible. To do this, you have enlisted the help of k reviewers. Each reviewer i has a cost s;; for writing a
review for paper j. The strategy of each reviewer i is to select a subset of papers to write a review for. They can select
any subset S; C {1,2,...,n}, as long as the total cost to write all reviews is less than T (the time before the deadline):
E Sij <T.
jeS
Reviews are costly, so you want to reward them for their efforts. However, each paper and review has to be treated
equally: specifically, there is a budget of 1 for each paper, that will be evenly shared across all reviewers who reviewed
that
For example, if 4 reviewers reviewed a paper they will receive 1/4 each. If only one reviewer reviews
раper.
the paper they will receive all the reward. Of course, each reviewer i wants to maximize their utility u;, which is the
reward R; over all papers they receive minus the effort they put into writting reviews:
U; = R; – Sij.
jeSi
You can assume that for the given s;;'s, there is a combination of strategies S; where every reviewer has positive
utility and all papers get at least one review. However, this outcome might not be a pure Nash equilibrium. As a
designer, your goal is to find the fraction of papers that receive at least 1 review at a pure Nash equilibrium, for the
worst possible combination of s;,'s satisfying the assumption.
(a) Show that there exists a set of sij's such that the fraction of papers that receive reviews is close to 1/n.
Given the previous negative result, you think about increasing the reward of each paper from 1 to B > 1.
(b) Show that for B = 2 this fraction is close to 1/3. [Hint: You can consider an instance with 3n + 1
only n will be reviewed.]
раpers
and
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