MTH460 MTH 560 Homework assignments PDF

Preview

Summary

Download MTH460 MTH 560 Homework assignments PDF

Description

MTH 460/560

Exercise I

January 20, 2010

Prof. Cowen Definition: A strategy triple (s, t, u) in a 3-player game is a Nash Equilibrium if each player’s strategy is a best response to the other two players’ strategies. So, s is a best response for Player 1 if Player 2 uses t and Player 3 uses u; t is a best response for Player 2 if Player 1 uses s and Player 3 uses u; and u is a best response for Player 3 if Player 1 uses s and Player 2 uses t. Exercise 1: Consider the following 3-person game: P3 u1

u2

P2

P2

t1

t2

t1

s1 (45, 50, 9) (45, 49, 3) (45, 53, 10)

t2 (45,52,8)

P1 s2 (48, 46, 2)

(0, 47, 4)

(48, 48, 0)

(46, 50, 5)

(3, 41, 2)

(48, 47, 3)

(0, 52, 0)

(1, 50, 2)

s3

i) Indicate Player 1’s best responses by circling them, indicate Player 2’s best responses by putting a square around them, and indicate Player 3’s best responses by putting a triangle around them. ii) Find all Nash equilibria.

MTH 460/560

Exercise II

February 13, 2013

Prof. Cowen Exercise 2: Consider the following two person strictly competitive game G with perfect information

a I

l1

L1

d I

l2 r2 u1

u2

l3 u2

r1

b II

c II

R1

L2

e I

f I

r3 u1

l4 u3

R2

g I

r4

l5

u4

u1

r5 u4

Find the restriction of the strategy pair (ℓ1 r2 ℓ3 r4 ℓ5 , R1 L2 ) to the subgame: 1) Gb

2) Gc

3) Ge...