Models of breaking-up
based on multiple games
5141209056
Contents
1. Introduction . !
2. The breaking-up model and the strategy analysis . !
2.1Both M and N love each other . 3
2.1.1 Basic model . 3
2.1.2 Extension of the basic model(Centipede game. 4

Backward Induction and Subgame Perfection
Xiaoshu Xu
Econ Dept, ACEM
November 16, 2012
X.Xu (ACEM)
Backward Induction and Subgame Perfection
11/16
1 / 17
Deciency of NE
Example
player 2
L
R
player 1 A 1, 2 1, 2
B 0, 0 2, 1
X.Xu (ACEM)
Extensive form
Backw

Perfect Bayesian Equilibrium
Xiaoshu Xu
Econ Dept, ACEM
December 21, 2012
X.Xu (ACEM)
Perfect Bayesian Equilibrium
12/21
1/9
Conceptual Weakness
The concept of subgame perfect is not strong enough to select out
BNEs that are sequentially rational in dynam

Incomplete Information
Xiaoshu Xu
Econ Dept, ACEM
November 30, 2012
X.Xu (ACEM)
Incomplete Information
11/30
1 / 10
Incomplete Information
Imperfect information is only one way that players can be
asymmetrically informed.
Example: bargain
We can say there

Repeated Games
Xiaoshu Xu
Econ Dept, ACEM
November 23, 2012
X.Xu (ACEM)
Repeated Games
11/23
1 / 10
Repeated Games
Reasons for modeling repeated games.
A repeated game is a normal-form game (stage game) that is played
repeatedly over discrete time periods

Conditional Probabilities and BayesRule
Xiaoshu Xu
Econ Dept, ACEM
December 14, 2012
X.Xu (ACEM)
Conditional Probabilities and BayesRule
12/14
1/5
Beliefs
We need to compute a players expected payo to evaluate sequential
BayesRule
Pr(AjB ) =
Example
X.Xu

Game Theory Spring 2014
Assignment 3
1. Consider a simple simultaneous-bid poker game. First, nature selects numbers x1 and
x2 . Assume that these numbers are independently and uniformly distributed between
0 and 1. Player 1 observes x1 and player 2 obser

Homework #1
1. Consider the nine-region location game presented in Chapter 8, where two vendors
simultaneously choose locations and then customers walk to the nearest vendor to purchase a
single unit. That is, the strategy space for each player i is Si =

Mixed Strategy Nash Equilibrium
Xiaoshu Xu
Econ Dept, ACEM
November 2, 2012
X.Xu (ACEM)
Mixed Strategy Nash Equilibrium
11/02
1/9
Matching Pennies
player 2
H
player 1 H 1, 1
T
1, 1
T
1, 1
1, 1
Only at the strategy ( 12 , 12 ) can a player not be outwitted

Oligopoly Game and Voting Games
Xiaoshu Xu
Econ Dept, ACEM
October 26, 2012
X.Xu (ACEM)
Oligopoly Game and Voting Games
10/26
1/8
Cournots Model
Suppose there are two rms, producing an identical good. The
strategic choice is quantity, Si = fqi : qi
0g. Th

Introdution to Game Theory
Xiaoshu Xu
Econ Dept, ACEM
September 14, 2012
X.Xu (ACEM)
Intro to Game Theory
09/14/12
1/8
Facts from Wikipedia
Interactive decision theory
Widely applied in economics, political science, psychology, logic and
biology.
Eight ga

Normal Form Games
Xiaoshu Xu
Econ Dept, ACEM
Sept 21, 2012
X.Xu (ACEM)
Normal Form Games
09/21/12
1 / 14
Strategies
Denition: a complete contingent plan for a player in the game.
Extensive form: a strategy must specify the action that a player
would take

Mixed Strategies and Expected Payos
Xiaoshu Xu
Econ Dept, ACEM
Sept 28, 2012
X.Xu (ACEM)
Mixed Strategies and Expected Payos
09/28/12
1 / 10
The source of mixed strategies
Strategic uncertainty: we may not be certain which particular strategy
a player wil

Dominance and Best response
Xiaoshu Xu
Econ Dept, ACEM
October 5, 2012
X.Xu (ACEM)
Dominance and Best response
10/05/12
1/9
Example 1
player 2
player 1 U
D
L
2, 3
1, 0
R
5, 0
4, 3
For player 1, U yields higher payl than D, no matter what strategy
player 2

Nash Equilibrium
Xiaoshu Xu
Econ Dept, ACEM
October 19, 2012
X.Xu (ACEM)
Nash Equilibrium
10/19
1/7
Nash Equilibrium
For many games, common knowledge of rationalizability cannot pin
down a unique strategy prole.
A Nash equilibrium is a strategy prole in w

Rationalizability and Iterated Dominance
Xiaoshu Xu
Econ Dept, ACEM
October 12, 2012
X.Xu (Institute)
Rationalizability and Iterated Dominance
10/12
1/8
Common Knowledge of Rationalizability
player 2
player 1 A
B
X
3, 3
0, 0
Y
0, 5
3, 1
Z
0, 4
1, 2
Player

Details of the Extensive Form
Xiaoshu Xu
Econ Dept, ACEM
November 9, 2012
X.Xu (ACEM)
Details of the Extensive Form
11/09
1/7
A Game Tree
A game tree consists of nodes and branches
successor node, predecessor node and initial node
Tree rules 1-4
Tree rule

Game Theory Spring 2014
Assignment 2
The due date for this assignment is .
1. Suppose a parent and child play the following game, rst analyzed by Becker (1974).
First, the child takes an action, A, that produces income for the child, IC (A), and
income fo