10HW4

# 10HW4 - a,b,c> 0 and a> c Suppose we expand the...

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Economics 104B Problem Set #4 (Due June 3) Spring 2010 1. a) Suppose your opponent is not playing her Nash equilibrium strat- egy. Should you play your Nash equilibrium strategy? Why or why not? b) Choose from the following the reason or reasons to adopt a Nash equilibrium strategy: (i) I can do the best regardless of what the other player does; (ii) Even if the other player knows my strategy, she cannot take advantage of that information; (iii) I will not regret to play the strategy if I expect the other player to play her Nash equilibrium strategy and my expectation turns out to be correct. Explain brieﬂy why Nash equilibrium represents a plausible outcome of a game. 2. Consider Bertrand duopoly with a homogenous good. Market demand is p ( Q ) = a - bQ . Firms have the same constant marginal cost c and zero ﬁxed cost. Assume

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Unformatted text preview: a,b,c > 0 and a > c . Suppose we expand the strategies to allow each ﬁrm to independently and simultaneously quote a price with the provision that it matches any low price. Show that the strategy proﬁle in which each ﬁrm quotes the monopoly price is a Nash equilibrium. Is there any other Nash equilibrium? 3. Two ﬁrms are in the chocolate market. Each can choose to go for the high end of the market (high quality) or the low end (low quality). Resulting proﬁts are given in the following table: Firm 1 Firm 2 High Low High 50, 50 100, 800 Low 900, 600-20, -30 1 a) How many Nash equilibria does the game have? Support your answer. b) How much would ﬁrm ﬁrm 1 need to oﬀer ﬁrm 2 to persuade it to collude? Support your answer. 2...
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## This note was uploaded on 08/27/2011 for the course ECON 104 taught by Professor Staff during the Spring '10 term at UCSB.

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10HW4 - a,b,c> 0 and a> c Suppose we expand the...

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