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1. Suppose that diffusion occurs via the "threshold" procedure in Beaman et al. (2018). N agents are arranged in an arbitrary, connected network. (a) Suppose the threshold is 3. Some agents are already infected in the network, but agent i is not. How do you determine how many additional nodes will be infected, assuming you can infect agent i? In which case is this equal to 0? (b) If K > 1, which types of agents can never be infected, regardless of who else is infected first? (c) For this part as well as (d)-(e), suppose the network is a tree. Assuming every agent adopts a new technology in the period after seeing 1 of their neighbors adopt, which agent should you target in order to spread adoption the fastest? The slowest? (d) Suppose that information spreads via a threshold model with a threshold of K = 2. You are allowed to strategically choose 2 agents for early adoption. Which two agents should you choose, and what will the pattern of final adoption look like? (e) (Harder) For K > 2, you are allowed to seed K agents, where K is the adoption threshold. Which K agents should you target, and what will the pattern of final adoption look like? (Hint: Final adoption will depend on network structure Consider a line and a star

1. Suppose that diffusion occurs via the "threshold" procedure in Beaman et al. (2018). N agents are arranged in an arbitrary, connected network. (a) Suppose the threshold is 3. Some agents are already infected in the network, but agent i is not. How do you determine how many additional nodes will be infected, assuming you can infect agent i? In which case is this equal to 0? (b) If K > 1, which types of agents can never be infected, regardless of who else is infected first? (c) For this part as well as (d)-(e), suppose the network is a tree. Assuming every agent adopts a new technology in the period after seeing 1 of their neighbors adopt, which agent should you target in order to spread adoption the fastest? The slowest? (d) Suppose that information spreads via a threshold model with a threshold of K = 2. You are allowed to strategically choose 2 agents for early adoption. Which two agents should you choose, and what will the pattern of final adoption look like? (e) (Harder) For K > 2, you are allowed to seed K agents, where K is the adoption threshold. Which K agents should you target, and what will the pattern of final adoption look like? (Hint: Final adoption will depend on network structure Consider a line and a star

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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4. Suppose that diffusion occurs via the "threshold" procedure in Beaman et al. (2018). N agents are arranged in an arbitrary, connected network. (a) Suppose the threshold is 3. Some agents are already infected in the network, but agent i is not. How do you determine how many additional nodes will be infected, assuming you can infect agent i? In which case is this equal to 0? (b) If K > 1, which types of agents can never be infected, regardless of who else is infected first? (c) For this part as well as (d)-(e), suppose the network is a tree. Assuming every agent adopts a new technology in the period after seeing 1 of their neighbors adopt, which agent should you target in order to spread adoption the fastest? The slowest? (d) Suppose that information spreads via a threshold model with a threshold of K = 2. You are allowed to strategically choose 2 agents for early adoption. Which two agents should you choose, and what will the pattern of final adoption look like? (e) (Harder) For K > 2, you are allowed to seed K agents, where K is the adoption threshold. Which K agents should you target, and what will the pattern of final adoption look like? (Hint: Final adoption will depend on network structure. Consider a line and a star network to aid intuition.)
Transcribed Image Text:4. Suppose that diffusion occurs via the "threshold" procedure in Beaman et al. (2018). N agents are arranged in an arbitrary, connected network. (a) Suppose the threshold is 3. Some agents are already infected in the network, but agent i is not. How do you determine how many additional nodes will be infected, assuming you can infect agent i? In which case is this equal to 0? (b) If K > 1, which types of agents can never be infected, regardless of who else is infected first? (c) For this part as well as (d)-(e), suppose the network is a tree. Assuming every agent adopts a new technology in the period after seeing 1 of their neighbors adopt, which agent should you target in order to spread adoption the fastest? The slowest? (d) Suppose that information spreads via a threshold model with a threshold of K = 2. You are allowed to strategically choose 2 agents for early adoption. Which two agents should you choose, and what will the pattern of final adoption look like? (e) (Harder) For K > 2, you are allowed to seed K agents, where K is the adoption threshold. Which K agents should you target, and what will the pattern of final adoption look like? (Hint: Final adoption will depend on network structure. Consider a line and a star network to aid intuition.)
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