ECO502/EE698A

ECO502/EE698A - Assignment #2 Due 18.1.12

1. Consider the following model of price competition. Two ﬁrms set prices in a market whose demand curve is given by the equation Q=6−p where p is the lower of the two prices. If ﬁrm 1 is the lower priced ﬁrm, then it is ﬁrm 1 that meets all of the demand; conversely, the same applies to ﬁrm 2 if it is the lower priced ﬁrm. In case they post the same price they each get half the market. Prices can only be quoted in dollar units, such as 0, 1, 2, 3, 4, 5, or 6 dollars. Suppose, furthermore, that costs of production are zero for both ﬁrms, and each ﬁrm aims to maximize its own proﬁts. (a) Write down the strategic form of this game. (b) Is there a strictly dominant strategy
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If more than one vendor is at the same location, they split business evenly. (a) Consider a game in which two ice-cream vendors pick their locations simultaneously. Show that there exists a unique pure strategy Nash equilibrium and that it involves both vendors locating at the midpoint of the boardwalk. (b) Show that with three vendors, no pure strategy Nash equilibrium exists. 4. (Altruistic preferences) Person 1 cares both about her income and about person 2’s income. Precisely, the value she attaches to each unit of her own income is the same as the value she attaches to any two units of person 2’s income. How do her preferences order the outcomes (1,4), (2,1), and (3,0), where the ﬁrst component in each case is person 1’s income and the second component is person 2’s income? Give a payoﬀ function consistent with these preferences. 5. Mr. Poorman acquires a lottery ticket that with equal probabilities will be worth INR 20,000 or 0. His von Neumann-Morgenstern utility function is the square root of his wealth. In the absence of the lottery ticket, his wealth is X. He is oﬀered an opportunity to sell this ticket for INR 9000. How large does X need to be in order to refuse this oﬀer? Mr. Richman whose von Neumann-Morgenstern utility function is the square root of his wealth is considering buying this lottery ticket from the poor fellow for a price of 9,000 ducats. How wealthy does the rich fellow have to