3. Consider a "star" network of K≥ 2 agents. Label Agent 1 as the "central" agent. (a) Suppose that all agents update according to a DeGroot process whereby they equally weight their own and their neighbors' information. Completely characterize the updating matrix A. Note that this is not the same as the adjacency matrix. (Hint: Your answer should state entries as a function of K.) (b) Agents 2,..., K are all similarly-situated in the network. What should be true of their social influence? (c) Using your answer to (b), derive the social influence for each player (Note that this will be a function of K). Comment on how the influence of the central agent changes as K increases.

3. Consider a "star" network of K≥ 2 agents. Label Agent 1 as the "central" agent. (a) Suppose that all agents update according to a DeGroot process whereby they equally weight their own and their neighbors' information. Completely characterize the updating matrix A. Note that this is not the same as the adjacency matrix. (Hint: Your answer should state entries as a function of K.) (b) Agents 2,..., K are all similarly-situated in the network. What should be true of their social influence? (c) Using your answer to (b), derive the social influence for each player (Note that this will be a function of K). Comment on how the influence of the central agent changes as K increases.

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

Problem 1PE

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