Homework2NWLife10

Homework2NWLife10 - NetworkedLife(CIS112,Spring2010...

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Networked Life (CIS 112), Spring 2010 Prof Michael Kearns Homework 2 Issued April 13, 2010. Due as hardcopy in class Tue April 27. Don’t forget to staple and write your name. 1. (20 points) Consider diagrams of the kind discussed in Schelling’s “Micromotives and Macrobehavior” (see Figure 1, page 104 for an example), for modeling activities in which the number of people participating at the current round (the y axis) is a function of the number participating at the last round (the x axis). a. Carefully draw such a diagram in which there are 3 stable equilibria and 2 unstable equilibria. b. Carefully draw such a diagram in which there are 3 stable equilibria and 4 unstable equilibria. c. What can you say in general about the relationship between the number of unstable and stable equilibria in such models? 2. (20 points) Consider the hypothetical spread of a disease on a network. Each vertex represents an individual person who may or may not decide to receive a vaccination. Each edge represents potential contact between a pair of people. A person can contract the disease from any of his
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