Problem 1 States Of Nature 10 Points Consider The Following Variant Of The Prisoner S Dilemma Guido And Luca Work F 1 (156.18 KiB) Viewed 71 times
Problem #1: States of nature (10 points) Consider the following variant of the Prisoner's Dilemma: Guido and Luca work for a mob boss named Vito, who is unpredictable. Vito is not a player in this game, but when Guido and Luca are arrested, Vito may be Nice, with probability p, or Nasty, with probability 1 - p. Game tables for the two states are shown below: Vito is Nice (p) Luca Testify Quiet Testify -10,-10 0, -20 Quiet -20,0 -1,-1 Vito is Nasty (1-P) Luca Testify Quiet Testify -40, -40 -20, -20 Quiet -20, -20 -1,-1 Guido Guido a) First, assume that p=0.5, so that Vito is equally likely to be Nice or Nasty. Combine these two game tables into one table containing Guido and Luca’s expected payoffs, then find all of the pure-strategy Nash equilibria in this game.
b) Now, assume that p is unknown. Once again, combine the two game tables into one table containing Guido and Luca's expected payoffs. (Hint: These expected payoffs will have to be written in terms of p.) c) Based on your answer to b), for what values of p is (Quict, Quiet) a Nash equilibrium?
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