Statistics 155: Game Theory Fall 2016 - Discussion 4
Definition 1. Let G = (X, Y, A) be a finite game, and let g be a one-to-one transformation
of Y onto itself. The game G is said to be invariant under g if there is a unique g, a
one-to-one transformatio

Statistics 155 Homework Assignment 5 (due Tuesday, October 18, 2016)
1. (Series and parallel games) Karlin and Peres, Exercise 3.1, p72.
(Note: As well as giving the value of the game, specify optimal strategies for the Troll and the Traveler.)
2. (Two-pl

Stat 155 Midterm Spring 2014
Name:
SID:
This exam has 5 problems and a total of 75 points. Attempt all questions and show your
working - solutions without explanation will not receive full credit. One double sided sheets
of notes are permitted. Answer que

Statistics 155: Game Theory Fall 2016 - Discussion 1
Definition 1. Recall from Stat 134 that the expectation of a random variable X is the
mean of the distribution of X, denoted E(X).
If X is a discrete random variable, then
X
E(X) =
x P (X = x).
x
If X

Stat 155 Midterm Practice Solutions
Problems:
Attempt all questions and show your working - solutions without explanation will not receive
full credit. One double sided sheets of notes are permitted.
Q 1 Find the value and optimal strategy of the followin

Statistics 155: Game Theory Fall 2016 - Discussion 2
Definition 1. A combinatorial game in which the legal moves in some positions, ot the sets
of winning positions, differ for the two players, are called partisan.
Example of partisan games: Chess, Hex, t

Midterm 1
Stat155
Game Theory
Lecture 11: Midterm 1 Review
This is an open book exam: you can use any printed or written material,
but you cannot use a laptop, tablet, or phone (or any device that can
communicate). There are three questions, each consisti

Stat 155 Midterm Spring 2014
Name:
SID:
This exam has 5 problems and a total of 75 points. Attempt all questions and show your
working - solutions without explanation will not receive full credit. One double sided sheets
of notes are permitted. Answer que

Statistics 155 Homework Assignment 2 (due Thursday, September 15, 2016)
1. (Up-and-down Rooks) Karlin and Peres, Exercise 1.7, p33.
2. (A partisan subtraction game)
Consider the subtraction game in Example 1.2.1 (Karlin and Peres, p21).
(a) Show that, fro

Outline for today
Stat155
Game Theory
Lecture 6: Solving two player zero-sum games
Zero sum games
Recall: payoff matrices, mixed strategies, safety strategies, Von
Neumanns minimax theorem
Solving two player zero-sum games
Saddle points
Dominated pure str

Outline for today
Stat155
Game Theory
Lecture 7: two player zero-sum games
Zero sum games
Recall: payoff matrices, mixed strategies, von Neumanns minimax
theorem
Solving two player zero-sum games
Recall: Saddle points, dominated pure strategies, equalizin

Outline for today
Stat155
Game Theory
Lecture 8: Symmetry in two player zero-sum games
Solving two player zero-sum games
Recall: definitions, solving 2 2, 2 n and m 2 games, principle of
indifference
Symmetry
Invariance of payoffs under permutations
Invar

Outline for today
Stat155
Game Theory
Lecture 5: Two player zero-sum games
Zero sum games
Pick-a-Hand
Other two-player zero-sum games
Payoff matrices, pure and mixed strategies
Safety strategies
Von Neumanns minimax theorem
Peter Bartlett
September 8, 201

Statistics 155 Homework Assignment 3 (due Thursday, September 22, 2016)
1. (A drinking game) Ferguson, Exercise 1.5 (4), pII-8.
2. (A 3x2 game) Karlin and Peres, Exercise 2.5, p51.
3. (2x2 games) John Williams The Compleat Strategyst presents the followin