Assignment 6 Solutions
The main point of this assignment is for you to develop an appreciation for equilibria. What exactly is
an equilibrium? What does it mean for one to be stable? Unstable? You will also note that question one is
Cody Beals (8cfb)
January 27, 2012
MATH 339: Assignment #3
1.a) Let Player 1 play strategy A with probability J and B with probability cfw_ . Jcfw_. Let Player 2 play A
with probability J and B with probability cfw_ . Jcfw_. The expected payoffs to Player
Assignment 2 Solutions
1. Look at you, playing games in real life!
2. These ve games were not chosen arbitrarily. These are ve of the most common symmetry, simultaneous, two-player games around. You see these in the research literature all
Assignment 4 Solutions
As it turns out, this assignment comprises some important lessons. I had not intended for this to be as
valuable as it is. What luck!
1. (a) The completely symmetric rock-paper-scissors game, where the payo to strategy A against B i
Assignment 3 Solutions
1. (a) We can write a general form for the payos in a 2x2 game quite succinctly. Observe: if player 1
plays strategy A with probability p (B with prob. (1 p) and player 2 plays A with prob q (B
with prob (1 q), then for
A a1 , a
Assignment 5 Solutions
1. The notes I posted recommend nding all symmetric Nash Equilibria rst and then investigating these
to see which correspond to evolutionary stable strategies. I prefer going straight to the denition of an
Denition 1 In an evol
Assignment 7 Solutions
All of these questions can be answered using the replicator equation
XA = XA (1 XA )(wA wB ).
This follows from the observation XB + XA = 1. This assignment is worth 20/20.
XA = XA (1XA )(wA wB ) = XA (1XA )(3XA +(1XA )(2XA +
Solutions to proto-nal
April 11, 2009
To Sue or settle
1. If you draw out the game tree you can quickly see that my expected
value for going to court is $75 million and McDonalds expected value
from going to court is $-78 million. So assuming we
Assignment 8 Solutions
1. For each of these questions, we need to appeal to the replicator-mutator equation:
XA = XA wA (1 ) + XB wB XA wave .
Keep in mind that XB = (1 XA ). Hence, this equation has only two variables, XA and . For
simplicity, Ill drop t
Page 1 of 9
Please read the following points carefully before proceeding!
1. Please note: Proctors are unable to respond to queries about the interpretation of exam questions. Do your b
MATH 339 Class Notes
How do populations grow?
Suppose we have two types of individuals in a population: type A and type B. Let nA (t)
and nB (t) be the number of type A and type B respectively in the population at the time t.
M AT H E M AT I C A L R E C R E AT I O N S
by Ian Stewart
A Puzzle for Pirates
If 50 percent or more are in favor, the
proposal passes and is implemented
forthwith. Otherwise the proposer is