Econ. 461
Fall 2015
H. Ofek
Problem Set #6
Maxminimization and Zero-sum Games
(Due:Wed. 10/28)
Readings in Dixit et al. text: pp. 21-22, 106-107, and Chaps. 7, 8.
1. Determine which (if any) of the following three games are strictly competitive.
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[HAPTER 4 STABLE PLAY: NASH EQUIUBRIA IN DISCRETE GAMES WITH TWO 0R THREE PLAYERS
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dimensions.
—Ouvea WENDELL HOLMES
Introduction
IN THtS CHAPTER, WE GO beyond two- and three—player games to consider a richer
:tl‘i‘tu of settings. This means examining not only! games
Introduction
Game theory is the study of situations of
conflict and cooperation
Sequential Games
What is a game?
A game is defined as a situation in which all the following components are in place:
1. At least two mindful players.
As distinct from mindle
Sequential Move Games
E. Zermelos theorem
Sequential Games
Zermelos theorem: In the game of chess there is
precisely one of the following three possibilities:
ECON 461 Fall 2014, H. Ofek
1. White has a winning strategy.
2. Black has a winning strategy.
3.
Repeated-Play Games
Part C: Finite repetition of unknown length
1
Repeated-play
Finite repetition of unknown length
We can use the discount factor to reinterpret the case of a repeated game that ends after a
random (i.e., a finite but unknown) number of r
3/28/2015
Oligopolistic Competition
B. Stackelbergs leadership model
1
Oligopoly.
First Mover Advantage
The Stackelberg leadership model differs from the Cournots duopoly in that output
decisions are made sequentially rather than simultaneously.
Firm 1
Game Theory
ECON 461
Spring Semester 2016
Time & Location: TTh, 10:05 am - 11:30 am, Science Library 302
Final Time & Location: TBA
Please see nal page for make-up nal policy!
Andreas Duus Pape
Department of Economics
Binghamton University
email: [email protected]
Repeated-Play Games
(Part A)
Repeated-play
The overall game & the stage game
Repeated games are played on two levels: the overall game and a
component game which is repeated.
The game which is repeated is called the stage game
o
typically, a finite simu
2/13/2015
Equilibrium
&
Nash Equilibrium
A. The notions of equilibrium and stability
Equilibrium
The Concept of Equilibrium
Equilibrium: A state of equilibrium is a situation in which
opposing forces that operate on a system are balanced and,
consequentl
3/25/2015
Oligopolistic Competition
A. Cournot's models
Oligopoly.
Cournot's models
Cournot's models are based on the expectation that each firm in an
industry maximizes profits assuming its competitors output remains
constant at the current level.
ECON
Mixed strategy Nash Equilibria
A. Introduction
Matching pennies
Player II
Heads
Player I
Tails
Heads
1,-1
-1, 1
Tails
-1, 1
1,-1
1
Mixed Strategy
Major Motivation for Mixed Strategies
The early extension of game theory from pure strategies to mixed strat
Strictly Competitive Games
and
Security (maxminimization) Strategies
Strictly Comp. Games
Security Level, Defined
Security level of a player in a game is the largest (expected)
payoff he or she can guarantee no matter what the other players
may do.
ECON
4/8/2015
Strategic moves
(Readings in Dixit et al. text: Chap. 10)
Strategic moves
Commitments, Threats & Promises
Strategic moves are first (or early) moves taken by players to
fix the rules of later play and thereby alter the equilibrium
outcome of the
Strictly Competitive Games
and
Security (maxminimization) Strategies
Strictly Comp. Games
Security Level, Defined
Security level of a player in a game is the largest (expected)
payoff he or she can guarantee no matter what the other players
may do.
ECON
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Econ. 461
Fall 2015
H. Ofek
Problem Set #4
Follow-up Questions
Question 1:
1. Players II best response to strategy s1 by player I is
(a) t1;
(b) t2;
(c) t3;
(d) both t1 and t3;
(e) none of these.
2. Players II best response to strategy s2 is
(a) t1;
(b) t
Econ. 461
Fall 2015
H. Ofek
Problem Set #4
Best Response
Due: Wed. - 10/7/2015
Readings in Dixit et al. text: pp. 104 - 105, 133 - 163
1. Using the method of best response obtain the pure-strategy Nash equilibrium in the following game
(which is not domin
Econ. 461
Fall 2015
H. Ofek
Problem Set #5
Follow-up Questions
Question 1:
1.
(A): Which of the following pairs is a pure-strategy Nash equilibrium in game A?
(a)
(b)
(c)
(d)
(e)
2.
(BR).
(TL).
(TR).
(BL).
none of these.
(A): Which of the following pairs
Econ. 461
Fall 2015
H. Ofek
Problem Set #5
Mixed Strategy Equilibria
Due:Wed. 10/14/15
1.
Readings in Dixit et al. text: Chap. 7, and pp. 262-268.
Find all pure- and mixed-strategy Nash equilibria (if any) of the following games by constructing, in each c
Econ. 461
Fall 2015
H. Ofek
Problem Set #6
Follow up Questions
(Due: 28/10/2015)
Question 1:
1. [Q1] Which (if any) of the three games in this question is strictly competitive?
(a)
(b)
(c)
(d)
(e)
Game A, only.
Game B, only.
Game C, only.
Both A and C.
Bo
10/30/2015
Oligopolistic Competition
A. Cournot's models
Oligopoly.
Cournot's models
Cournot's models are based on the expectation that each firm in an
industry maximizes profits assuming its competitors output remains
constant at the current level.
ECON
Econ. 461
Fall 2015
H. Ofek
Problem Set #7 Follow up Questions
Due Tue. 11/6/2015
Question 1:
Follow-up questions 1 to 3 below refer to the situation in which DMC is a monopoly.
1.
[Q1-(a)]: p = (a) 36;
(b) 48;
2.
[Q1-(a)]: QDTC = (a) 36;
3.
[Q1-(a)]: = (
Econ. 461
Fall 2015
H. Ofek
Problem Set #7
Oligopolistic Competition
Due Fri. 11/6
Readings: Dixit et al. text: pp. 133 - 142
Pindyck & Rubinfeld, Chap. 12 (posted on Blackboard)
I. Cournots Models
1. (Cournots duopoly with a homogeneous product): Answer