2350pqset_5

# 2350pqset_5 - E N2 —A I NMENT l Centipede Game Tom and...

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Unformatted text preview: E N2 —A I NMENT l. Centipede Game: Tom and Jerry are playing the following game. There is an amount of \$10 in a magic basket. This basket makes the money in it double if it hears the word ‘Pass’. Tom and Jerry move sequentially, with Tom starting ﬁrst. Each person can choose to say either Stop (S) or Pass (P). If a person says Stop then the game is over and he gets 75% of the amount in the basket and the other person gets the remaining 25%. If a person says Pass then the amount in the basket doubles and it is the other person’s choice to pass again (and let the money double) or to stop the game and take 75% of the basket amount. Draw the extensive form of the game and ﬁnd the subgame perfect equilibrium if a maximum of eight passes is allowed. 2. Hungry Lions: A Lion is considering whether to eat its easy—to—catch prey (E) or let it pass (P). If he lets it pass, he will be hungry but if he eats it he will be slow and can be eaten by another lion that will come by. If the second lion eats the ﬁrst lion then the second lion can be eaten by the third lion that will come by. If the third lion eats the second then he can be eaten by the fourth etc. (a) Draw the extensive form of this game and ﬁnd its he subgame perfect equilibrium if there is a total of two lions. (b) Draw the extensive form of this game and ﬁnd its he subgame perfect equilibrium if the number of lions is 3. 3. Suppose the supply side of a market consists of 2 identical ﬁrms with costs 61(q1) = 2q1 and 62 ((12) 2 Zn. Market demand is given by gzll—p (a) Calculate the Cournot equilibrium in this market. (b) Calculate the Stackelberg equilibrium assuming ﬁrm 1 is the leader and ﬁrm 2 is the follower. (c) By comparing the proﬁts each ﬁrm makes under the two scenarios, show that the ‘leader’ has an advantage in quantity competition. Explain intuitively. 4. Samaritan’s Dilemma: Consider the followig game between a parent and a child. After the child decides how many hours to work (L) and so his income is Y = 10L, the parent observes Y and decides how much money to transfer to the child (t). The child’s utility function is U0: 10L—L2/2+t where L is the labour time of the child, Y = 10L is his income at a wage of 10, L2 / 2 is his disutility from working, and t is the amount that he will be given by the parent to the child. The parent’s utility function is Up = min(X — t,Y+t) where X = 100 is the parent’s income. Thus, the parent wishes to improve the child’s utility by giving it t dollars, up to the point where the child’s and the parent’s income are equal after the transfen (a) Find the subgame perfect Nash equilibrium and the efﬁcient outcome and compare them. (b) Suppose the parent declares the transfer t to the government and so the child is taxed such that half of the t amount is taken by the government, that is, a tax rate of 50% is applied on t. This is known to the child before he makes his labour choice. Find the subgame perfect equilibrium in this case and compare it to the equilibrium in part (a). ...
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