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...

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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 $

Extracted 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 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

Jun 08, 2022

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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...

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