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homework2 - Networks Spring 2010 David Easley and Jon...

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Networks: Spring 2010 Homework 2 David Easley and Jon Kleinberg Due February 19, 2010 As noted on the course home page, homework solutions must be submitted by upload to the CMS site, at https://cms.csuglab.cornell.edu/. This means that you should write these up in an electronic format (Word files, PDF files, and most other formats can be uploaded to CMS). Homework will be due at the start of class on the due date, and the CMS site will stop accepting homework uploads after this point. We cannot accept late homework except for University-approved excuses (which include illness, a family emergency, or travel as part of a University sports team or other University activity). Reading: The questions below are primarily based on the material in Chapters 6 and 8 of the book. (1) In this question we will consider several two-player games. In each payoff matrix below the rows correspond to player 1’s strategies and the columns correspond to player 2’s strategies. The first entry in each box is player 1’s payoff and the second entry is player 2’s payoff. (a) Find all Nash equilibria for the game described by the payoff matrix below. Player 1 Player 2 L R U 0 , 0 3 , 4 D 1 , 3 5 , 1 (b) Find all Nash equilibria for the game described by the payoff matrix below. Player 1 Player 2 L R U 1 , 1 3 , 2 D 0 , 5 4 , 3 [Hint: This game has a mixed strategy equilibrium. To find the equilibrium let the probability that player 1 uses strategy U be p and the probability that player 2 uses strategy L be q . As we learned in our analysis of Matching Pennies, if a player uses a mixed strategy (one
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