b. Show that choosing the number 5 is a dominated strategy_ Hint: what would class average K have to be for the target number to be 5?] c. Show that choosing the number 90 is a dominated strategy. (1. What are all of the dominated strategim '5' e. Suppose Elsa believes that none of her classmates will play the dominated strategies found in part (d). Given these beliefs what strategies are never a best response for ELsa'.' 7. Consider the policy advice game with the following payoff matrix . Suppose that the typcss and t of the expert are equally likely and that the expert can send either mxssage m or n. Recall that each cell of this payoff matrix records both the expert's and the policy maker's payoff from the corresponding type action combination a b c s 3,3 0," 2,2 t 0,0 3,3 2.2 a. If type .4 sends mtssage m with probability .3 and type f sends message 1'1 with probability .55, what is the posterior belief of the policy maker when he observe: message In? Use Bayes's rule to find your answer. b. Is there a Nash equilibrium in which type 3 sends message m with probability .6 and type f. sends missage n with probability .55? c. Is there a Nash equilibrium in which type 5 sends message m with probability . and type 1'- stmds massage n with probability .0? 8. Consider the used car market for the 20fi Touareg drmi'md in Lecture Note lThere is now a surge in demand for used Touareg; buyers would now be willing to pay up to $18,000 for an orange and $8,!Il0 for a lemon . All else remains identical to the example in Lecture Note 5. a. What price would buyers be willing to pay for a 2006 Touareg of unknown type if the fraction of oranges in the population were (Mi? h. Will there be a market for oranges if the fraction of oranges in the population is 0.6? Explain . c. \"rhat price would buyers be willing to pay if the fraction of oranges in the population is 0.2? (1. Will there be a market for oranges if the fraction of oranges in the population is ".2? Explain . e. What is the minimum value of the fraction of oranges in the population such that the market for oranges does not collapse '3 9. Glasser and [llearsmooth compete in the local market for windshield repairs . The market size [total available profits) is $10 million per year. Each firm can choose whether to advertise on local television . If a rm chooses to advertise in a givtm year it ecsts that form 83 million . If one rm 1| advertises mid the other does't ,then the former captures the whole market . If both rms advertise , they split the market 50:50. If both rms choose not to advertise , they also split the market 50:50. a. Suppose the two windshieldrepair firms know they will compete for just one year. Write down the payoff matrix for this game. Find the Nash equilibrium strategits
