ECOS3012 Lecture 1
ECOS3012 Lecture 1
August 10, 2021
Outline
Introduction
What is game theory
Logistics
Static games with complete information
How to define a game
How to solve a game
Examples
What we do in this unit: game theory
The subject of study
Multi-person decision problems
Individuals’ decisions influence each other’s welfare
Method of study
Models: capture the main ingredients of a strategic situation
How do we proceed?
Create a model to describe a situation
Solve the game to make a prediction about what will happen
Compare the solutions with what happens in experiments/real-life situations
Modify the model/solution concept
What we do in this unit
One Round of act
Yes No
Complete Information? Yes I II
No III IV
Four types of games:
Static games with complete information
Dynamic games with complete information
Static games with incomplete information
Dynamic games with incomplete information
Warnings
This unit is very mathematical, and it demands a great deal of logical thinking
We study multi-person interaction at an abstract level If you are more interested in applications of game theory in business, please consider ECOS2201, ECOS3003, ECOS3005
Be prepared to work 9-12 hours per week to do well in this unit
You will not be able to take ECOS3901, if you take this unit
Class logistics
Lectures: 9-11 am on Tuesdays
Tutorial sessions: starting from week 2
Office hours:
2-3 pm on Mondays or by appointment
Personal room meeting ID: 527 116 1273
Assessment:
Weekly quizzes (10%): Form study groups, not timed, unlimited attempts
Mid-term exam (40%): In class in week 8, open book
Creative project (20%): Due in Week 12 (project) and 13 (peer-review)
Final exam (30%): Exam period, open book
Assessment: Weekly quizzes (10%)
10 Quizzes
Due Monday (almost) every week
No time limit, unlimited attempts
Test your understanding of the lectures
Prepare you for mid-semester and final exams
Answers are posted on Tuesdays
Assessment: Creative project (20%)
Two options
Become a teacher of game theory
Write an article about an observation of real life that can be explained by game theory
Individual or group (<= 3 people) submission
Join live lectures and tutorial sessions to know your classmates
On the content of the second half of the unit
Due Friday of Week 12
Peer-review due Friday of Week 13
More details after the mid-semester exam
Class logistics
How to contact the lecturer (Mengke)
Email: mengke. .au
Office hours: Mondays 2-3 or by appointment
Emails are not for questions, post on Ed Forum
How to contact the tutor (Robert)
Email: .edu.au
Consultation hours: Mondays 4 – 5 pm or by appointment
Make use of the Ed discussion board
Use the discussion board to ask questions
Search before you post
Heart questions and answers you find useful
Answer questions you feel confident answering
Share interesting course related content with staff and peers
The discussion board is monitored by the tutor and the lecturer
Questions?
Next: Static games with complete information
How to define a game?
How to solve a game?
Static games with complete information
How to define a game (or a strategic situation)?
Specify the following elements mathematically.
Players:
Set of strategies for each player:
Payoff function for each player:
Alternatively, for simple games (<= 3 players, finite strategies), use a table.
Example: Prisoner’s dilemma
The strategic situation:
Two prisoners, locked up in separate rooms, making decisions separately
If neither confess, then no evidence, minor penalty for both
If one confesses, then the confessor goes for free and the other gets severe penalty
If both confess, then both get moderate penalty
Example: Prisoner’s dilemma
What is a prisoner’s dilemma game?
Specify:
Set of players:
For each player, set of strategies:
For each player, payoff function:
Example: Prisoner’s dilemma
Prisoner 2
Not confess Confess
Prisoner1 Not confess -1, -1 -9, 0
Confess 0, -9 -6, -6
Alternatively, use a table.
Example: Stag hunt
Two hunters, simultaneously decide whether to go for a stag or a hare
It takes two persons to take down a stag, but only one person to get a hare
Both hunters prefer stag over hare
Hunter 2
Stag Hare
Hunter 1 Stag
Hare
Example: The battle of the sexes
Ann and Bob separately decide where to go for the evening: Opera or Football
Ann prefers Opera, Bob prefers Football
But they both prefer to be together
Bob
Opera Football
Ann Opera
Football
Example: Penalty Kick
Kicker and Goalkeeper simultaneously decide which direction to go (left or right)
Goalkeeper
Left Right
Kicker Left
Right
How to solve a game?
The goal is to make a prediction of the outcome of the game.
What is a reasonable/possible/plausible outcome of this strategic situation?
There are different ways to solve a game (different solution concept)
Different ways of thinking
Different predictions
What is a good solution concept?
Unique prediction?
Matches reality?
How to solve a game?
We introduce two solution concepts:
Iterated elimination of strictly dominated strategies (IESDS)
Nash equilibrium
Iterated elimination of strictly dominated strategies (IESDS)
Strictly dominated strategies:
No matter what others play, strategy s generates a lower payoff than strategy s’
Strategy s’ strictly dominates s
Strategy s is strictly dominated by s’
Elimination of strategy dominated strategies
Players are rational, therefore strictly dominated strategies should never be played
Iterated elimination
Suppose we know that player 1 never plays s (strictly dominated)
Then we can find whether player 2 has some strictly dominated strategies and delete them as well
Go back to player 1 again ……
IESDS: example
Player 2
Left Middle Right
Player 1 Up 1, 0 1, 2 0, 1
Down 0, 3 0, 1 2, 0
Steps:
Dominated strategies for Player 1: Nothing
Dominated strategies for Player 2: Right
Dominated strategies for Player 1: Down
Dominated strategies for Player 2: Left
Solution:
(Up, Middle)
IESDS
Order does not matter
Solution may not be unique
Player 2
L M R
Player 1 T 0, 4 4, 0 5, 3
M 4, 0 0, 4 5, 3
B 3,5 3, 5 6, 6
IESDS
Order does not matter
Solution may not be unique
Comments
Assumes that players do not play a strategy that is strictly worse: reasonable, sometimes too weak (Consider stag hunt, battle of the sexes, penalty kick)
Assumes that players know that others do not play SDS, know that others know that she knows that they do not play SDS…. : may be too strong
Beauty contest game
Pick a number between 0 and 100
Calculate the average of everyone’s number, and multiply it by 1/3
You win the game if your number is closer to the result
Enter your number now at the following survey page:
pingo.coactum.de/358349
Nash equilibrium
Best response:
Given the strategy profile of everyone else, the strategy that generate the highest payoff
Nash equilibrium:
A strategy profile
Every player best responds
Nobody has an incentive to deviate
NE: prisoner’s dilemma
Prisoner 2
Not confess Confess
Prisoner1 Not confess -1, -1 -9, 0
Confess 0, -9 -6, -6
NE: (Confess, Confess)
NE: battle of the sexes
Bob
Opera Football
Ann Opera 2, 1 0, 0
Football 0, 0 1, 2
NE: (Opera, Opera) and (Football, Football)
NE: stag hunt
Hunter 2
Stag Hare
Hunter 1 Stag 6, 6 0, 1
Hare 1, 0 1, 1
NE: (Stag, Stag) and (Hare, Hare)
NE: penalty kick
Goalie
Left Right
Kicker Left 0, 1 1, 0
Right 1, 0 0, 1
NE: No pure-strategy Nash
Nash Equilibrium
Pure strategy Nash equilibrium may not exist
May have multiple equilibria: prediction unclear
NE vs. IESDS
NE is a stronger solution concept than iterated elimination of strictly dominated strategies (IESDS).
Example:
Player 2
L M R
Player 1 T 0, 4 4, 0 5, 3
M 4, 0 0, 4 5, 3
B 3,5 3, 5 6, 6
NE vs. IESDS
NE is a stronger solution concept than iterated elimination of strictly dominated strategies (IESDS).
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