Stat 155 Game theory, Yuval Peres Fall 2004
Homework 10
Question 1:
Find the Nash equilibria in the game of ‘hawks and doves’, whose payoffs
are given by the matrix,
II D H
I
D (1,1) (0,3)
H (3,0) (-4,-4)
Question 2: a sequential congestion game. Six drivers will travel from
Ato D, each going via either Bor C. The cost in travelling a given road
depends on the number of drivers kthat have gone before (including the
current driver). These costs are displayed in the figure. Each driver moves
from Ato Din a way that minimizes his or her own cost. Find the total
cost. Then consider the variant where a superhighway that leads from Ato
Cis built, whose cost for any driver is 1. Find the total cost in this case
also.
A C
B D
k+12
k+12
5k+1 5k+1
Question 3: simultaneous congestion. There are two drivers, one who
will travel from Ato C, the other, from Bto D. Each road in the second
figure has been marked (x,y), where xis the cost is any driver who travels
the road alone, and yis the cost to each driver who travels the road along
with the other. Note that the roads are travelled simultaneously, in the
sense that a road is travelled by both drivers if they each use it at some
time during their journey. Write the game in matrix form, and find all of
the pure Nash equilibria.
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