hw3-key - 8.1 Let p be the probability that Row plays Up...

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8.1 Let p be the probability that Row plays Up, and q the probability that Column plays Left. Row’s expected payoffs from each strategy are EU U = 4q – (1 – q) = 5q – 1 EU D = q + 2(1 – q) = 2 – q If q = 1/2, Row is indifferent between the two strategies, if q > 1/2, Up gives a higher expected payoff, and if q < 1/2, Down gives a higher expected payoff. Row’s best response function is therefore Similarly, Column’s expected payoffs from each strategy are EU L = 1 – p EU R = 2p – (1 – p) = 3p – 1 If p = 1/2, Column is indifferent between the two strategies, if p > 1/2, Right gives a higher expected payoff, and if p < 1/2, Left gives a higher expected payoff. Column’s best response function is We can now graph these functions to create a best-response diagram and show the mixed-strategy Nash equilibrium, (p=1/2, q=1/2): 0.5 BR(q) 0.5 BC(p) NE p q The players’ expected payoffs can be found by plugging the equilibrium values of p and q back into one of the expected payoff equations used to find the equilibrium strategies: EU Row = EU U = EU D = 2 – q = 2 – 1/2 = 1.5 EU Column = EU R = EU L = 1 – p = 1 – 1/2 = 0.5
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8.2 (a) Using best-response analysis, we find two pure-strategy NE: (2, A) and (1, C). (b) Before calculating the equilibrium mix, it’s always best to see if any pure strategies are strictly dominated, and can therefore be eliminated (this greatly simplifies the analysis). In this case, D is dominated by C for column. B is never a best response for Column, but it is not strictly dominated by either A or C. In this sort of situation, it’s worth checking to see if B is strictly dominated by a mixed
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This note was uploaded on 10/15/2009 for the course ECON 122 taught by Professor Bonanno,g during the Summer '08 term at UC Davis.

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hw3-key - 8.1 Let p be the probability that Row plays Up...

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