Lecture 1 reminder
Econ 620
2016 Spring
pair
B
G
B
B,B
A,C
G
C,A
B+,B+
me
outcome matrix
outcomes payoffs
need to know my payoffs
need to know other players payoffs
Prisoners dilemma version of the game:
B
G
B
0,0
3,1
G
1,3
me
1,1
do not play a st
Lecture 11 reminder
Econ 1051
2016 Spring
Incredible threats
Game of entry to a market:
Two players: Entrant and Incumbent
First Entrant decides to enter or not
If enters then Incumbent decides whether to Fight or Accommodate
Not enter gives payoff 0 to E
Lecture reminders (FebMarch)
Econ
2016 Spring
Def A game of perfect information is one where, at each node, the player whose turn it is
knows which node she is at and how she got there.
Def a pure strategy for player I in a game of perfect information is
Lecture 15
Econ 620
Spring 2016
A game of conflict
 2 players choose F or Q simultaneously
 game ends at first Q if both F then continue
good news: if other person quits before you, you win $1 costs only if both F
bad news: each round both F, and loses
Economics 620
Game Theory with Applications
Spring 2016
Attila Ambrus
SYLLABUS
Location of Class: Biological Sciences 155
Meeting Time: Tu., Th. 10.05 11.20 am
Attilas Office hours: Wednesday 12.15 pm, Social Sciences 313
Attilas phone and email: 91966
Lecture 2 reminder
Econ 620
2016 Spring
Location choice model:
2 candidates
Simultaneously choose position on political spectrum 1,2, . . . ,10
Equal # of voters at each position, they vote for closest candidate (if tie then split equally)
Candidates to m
Lecture 6 reminder
Econ 620
2016 Spring
Bertrand model
2 firms, same market, but now set prices p [0,1]
Constant MC = c
0<c<1
Total demand Q(p) = 1 p
Demand for 1s product:
D1 ( p1 , p 2 )
1 p if p1 p 2
0
if p1 p 2
1 p2
if p1 p 2
2
Firms aim to maximize
Lecture 5 reminder
Econ 620
2016 Spring
If beliefs are correct: strategies are best responses to each other Equilibrium.
Definition A strategy profile s * ( s1* , , s *N ) is a Nash equilibrium (NE) if, for each i, her
choice si* is a BRi to the other pla
Lecture 10 reminder
Econ 620
2016 Spring
Another example for Evolutionary Stability
r
r
0,0
2,1
1,2
0,0
Q. Is any strategy ES
A. No no symmetric NE!
Q. So what happens in such games
Could be (i) genes mix
(ii) mix of genes
mix
popn mix polymorphic popula
Lecture 1618
Econ 620
Spring 2016
Finitely repeated games
Cooperation in Prisoners Dilemma
 Idea: repeated interaction might facilitate cooperation
C
D
C
2,2
1,3
D
3,1
0,0
Play x5
Analysis Q. How many subgames 1 + 4 +16 + 64 + 256
Q. How many strategi
Lecture23
Econ 620
Spring 2016
In class game: auctioning off coins
Q. What did you bid How many coins did you think were there?
Commonvalue auction
bid bi
true value v suppose highest bidder gets object and pays
payoff = v bi if bi is highest
0
else
(asy
Lecture 8 reminder
Econ 620
2016 Spring
CitizenCandidate Model
Voters are on a line
 evenly distributed
 vote for closest candidate
(1) # of candidates not fixed can enter or not
(2) cannot choose positions: know beforehand and as an assistant (track r
Question 1
C
D
C
(1,1)
(2,1)
a) False. One counterexample is Prisoners Dilemma.
D
(1,2)
(0,0)
Here s2 = D is a best response to s1 = C but s1 = C is strictly dominated.
b) False. The increase of player 1s payoff only affects player 2s mixed strategy wh
Practice Midterm
Attila Ambrus, Econ 620
Spring 2016
Question 1. [20 points] Short answer questions.
State whether each of the following claims is true or false (or can not be
determined). For each, explain your answer in (at most) short paragraph. Each
p
Lecture 2 reminder
Econ 620
2016 Spring
Location choice model:
2 candidates
Simultaneously choose position on political spectrum 1,2, . . . ,10
Equal # of voters at each position, they vote for closest candidate (if tie then split equally)
Candidates to m
Lecture 5 reminder
Econ 620
2016 Spring
If beliefs are correct: strategies are best responses to each other Equilibrium.
Definition A strategy profile s * ( s1* , , s *N ) is a Nash equilibrium (NE) if, for each i, her
choice si* is a BRi to the other pla
Lecture 6 reminder
Econ 620
2016 Spring
Bertrand model
2 firms, same market, but now set prices p [0,1]
Constant MC = c
0<c<1
Total demand Q(p) = 1 p
Demand for 1s product:
D1 ( p1 , p 2 )
1 p if p1 p 2
0
if p1 p 2
1 p2
if p1 p 2
2
Firms aim to maximize
Lecture 8 reminder
Econ 620
2016 Spring
New idea:
mixed strategies = randomization over pure strategies
e.g. R.P.S.
R
S
P
0,0
1,1
1,1
S
1,1
0,0
1,1
P
1,1
1,1
0,0
R
Q. Is there a BR in pure strategies?
No
BR(R) = P
BR(P) = S
Q. Is there a NE in mixed
A model of possibility and knowledge
Let us start with some finite set of states of the world . A state of the
world is very detailed: it specifies the physical universe, past, present
and future; what agents know, what they know about what others know, e
Proof of K1 () = cfw_ : () = (by the definition of ().
Proof of K2
( ) = cfw_ : () = cfw_ : () ()
= cfw_ : () cfw_ : ()
= () ()
Proof of K3 () we have () thus .
Proof of K4 By K3 we have ( () (). Also, () we have
() and () cfw_ : () . Therefore, ()
Lecture 3 reminder
Econ 620
2016 Spring
Rounds of iterated deletion correspond to: everyone is rational, everyone knows that
everyone is rational, everyone knows that everyone knows that everyone is rational, etc.
Limit of the procedure: common knowledge
Lecture 4 reminder
Econ 620
2016 Spring
Penalty shot game:
goalie
r
L
shooter
4,4
9,9
M
6,6
6,6
R
9,9
4,4
Eu1(L,p(r)
9
8
9
8
Eu1(M,p(r)
6
6
4
4
2
2
0
1
Eu1(R,p(r)
pr(r) belief
Middle is never best response
Definition Player is strategy si is a best
Lecture 9 reminder
Econ 620
2016 Spring
Evolution

Biological evolution: idea is successful strategies survive
In game theory:
Strategies = genes
Payoffs = genetic fitness
Influence of Bio on Econ
e.g. firm behavior as rules of thumb compete for survival
Reputation
1
An example with longrun players
Consider a game in which a player has two types, A and B. Imagine that if the
other players believe that is of type A, then s equilibrium payo will be much
higher than his equilibrium payo when the other playe