1. (49.2) Consider a voter i who prefers A to B. Fix a profile of votes a i for the other
voters. The provisional outcome given a i is what would happen if i did not participate
in the election and all other voters voted as in a i . There are two votes wh

1. In what follows let (x) be xs best friend.
(a) A strategy for player i specifies:
i. which student x would make an offer to if the teacher selects y.
ii. for each student x 6= y, whether x would accept ys offer if y made x an offer.
(b) Theorem 1 A str

Strategic Games
D EFINITION
A strategic game (with ordinal preferences) consists of:
a set of players
for each player, a set of actions
for each player, preferences over the set of action proles.
What Is an Action Prole?
We may assume that the set of play

1. .
(a) cfw_A, B
(b) cfw_(A, A), (A, B), (B, A), (B, B)
(c) (A, B) 1 (B, B) 1 (B, A) 1 (A, A).
(d) (A, A) and (B, B)
(e) It would be reasonable to say: I would pick A, because (A, A) is a Nash equilibrium, and
also the strategy profile which gives both p

Entry Game
An incumbent faces the possibility faces the possibility of
entry by a challenger.
The challenger may be a firm considering entry into an
industry currently occupied by a monopolist.
The challenger may be a politician competing for the
leadersh

Problem Set 1
September 26, 2015
Due date: 10/5/2015
Rules of the Game: students may form a group of at most 3 students. Each
group should hand in a single assignment, and must put the names of all people
in the group on the assignment. If there is disagr

Nash Equilibrium and Best Responses
D EFINITION
The action profile a is a Nash equilibrium if, for every player i,
ui (a ) > ui (ai , ai
) for every action ai of player i.
Bi (ai ) = cfw_ai Ai : ui (ai , ai ) > ui (ai0 , ai ), for all ai0 Ai
T HEOREM
The

Guess 2/3 of the Average
Each student submits a real number between 0 and 100.
All students whose numbers are closest to 2/3 of the average
evenly split $1. All other students get $0.
Assume that there are at least 2 students.
Guess 2/3 of the Average
T H

Problem Set 3
November 5, 2015
Due: 16 November 2015
Rules of the Game: students may form a group of at most 3 students. Each
group should hand in a single assignment, and must put the names of all people
in the group on the assignment. If there is disagr

ECON 4109H
LECTURE 9
M IXED S TRATEGY E QUILIBRIUM
October 16, 2014
Matching Pennies
H
T
H
1, -1
-1, 1
T
-1, 1
1, -1
players match ) player 2 prefers to switch choice.
players dont match ) player 1 prefers to switch choice.
So there is no Nash equilibrium

Coalitional Games
A Coalitional game is a model of interacting decision-makers
that focuses on behavior of groups of players.
For every group of players, there is a set of actions
. not only for individuals.
A group of players is a coalition.
The group of

Incomplete Information
Until now, we have assumed that all aspects of the game are
common knowledge.
In many situations, there is uncertainty about certain aspects
of the game or other players preferences.
In an auction, a bidder may be uncertain about th

Auctions: Ascending Auctions
Common Auction Form: People sequentially submit higher
bids for an object.
When no one wishes to submit a bid higher than the current
bid, the person making the current bid wins the object at the
price she bid.
Imagine each pe