hw3-key

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

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online