CS计算机代考程序代写 ECOS3012 Lecture 1

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). /docProps/thumbnail.jpeg