Dominant strategies Econ 171. Clicker Question 1, 3 5, 3 2, 4 7, 2 Player 2 Strategy A Strategy B Player 1 Strategy A Strategy B A ) Strategy A strictly.

Slides:

Advertisements

Similar presentations

The Random Dresser Wilbur has – 3 left shoes, all of different colors – 5 right shoes, all of different colors – 4 right gloves, all of different colors.

Advertisements

The Random Dresser (Clicker Question) Wilbur has – 3 left shoes, all of different colors – 5 right shoes, all of different colors – 4 right gloves, all.

Monte Hall Problem Let’s Draw a Game Tree… Problem 6, chapter 2.

Introduction to Game Theory Economics 171. Course requirements Class website Go to economics department home page. Under Links, find Class pages, then.

Basics on Game Theory Class 2 Microeconomics. Introduction Why, What, What for Why Any human activity has some competition Human activities involve actors,

BASICS OF GAME THEORY. Recap Decision Theory vs. Game Theory Rationality Completeness Transitivity What’s in a game? Players Actions Outcomes Preferences.

Clicker Question-A Chicken Game 0, 0 0, 1 1, 0 -10, -10 Swerve Hang Tough Swerve Hang Tough Player 2 Pllayer 1 Does either player have a dominant strategy?

Assoc. Prof. Yeşim Kuştepeli1 GAME THEORY AND APPLICATIONS DOMINANT STRATEGY.

© 2009 Institute of Information Management National Chiao Tung University Game theory The study of multiperson decisions Four types of games Static games.

The Stag Hunt Game. Introduction The stag hunt, first proposed by Rousseau, is a game which describes a conflict between safety and social cooperation.

Non-Cooperative Game Theory To define a game, you need to know three things: –The set of players –The strategy sets of the players (i.e., the actions they.

1 Chapter 14 – Game Theory 14.1 Nash Equilibrium 14.2 Repeated Prisoners’ Dilemma 14.3 Sequential-Move Games and Strategic Moves.

1 Game Theory. By the end of this section, you should be able to…. ► In a simultaneous game played only once, find and define:  the Nash equilibrium.

Taking Turns in the Dark (Subgame perfection with imperfect information) Econ 171.

Chapter 11 Game Theory and the Tools of Strategic Business Analysis.

Games What is ‘Game Theory’? There are several tools and techniques used by applied modelers to generate testable hypotheses Modeling techniques widely.

ECO290E: Game Theory Lecture 4 Applications in Industrial Organization.

An Introduction to Game Theory Part I: Strategic Games

Eponine Lupo.  Game Theory is a mathematical theory that deals with models of conflict and cooperation.  It is a precise and logical description of.

Check your (Mis)understanding? Number 3.5 page 79 Answer Key claims that: For player 1 a strictly dominates c For player 2, y strictly dominates w and.

Slide 1 of 13 So... What’s Game Theory? Game theory refers to a branch of applied math that deals with the strategic interactions between various ‘agents’,

Game Theory “Life must be understood backward, but … it must be lived forward.” - Soren Kierkegaard James Bednar.

A camper awakens to the growl of a hungry bear and sees his friend putting on a pair of running shoes, “You can’t outrun a bear,” scoffs the camper. His.

Algoritmi per Sistemi Distribuiti Strategici

Intro to Game Theory Revisiting the territory we have covered.

Problems from Chapter 3. Find Strategies for Simon.

Basics on Game Theory For Industrial Economics (According to Shy’s Plan)

Review of Yale Lectures 1 and 2 What is a strictly dominated strategy? Why should you never play one? Why do rational choices sometimes lead to poor decisions?

Reviewing Bayes-Nash Equilibria Two Questions from the midterm.

© 2008 Pearson Addison Wesley. All rights reserved Chapter Fourteen Game Theory.

Game theory The study of multiperson decisions Four types of games

1 Introduction APEC 8205: Applied Game Theory. 2 Objectives Distinguishing Characteristics of a Game Common Elements of a Game Distinction Between Cooperative.

UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Review Midterm3/19 3/12.

Nash Equilibrium Econ 171. Suggested Viewing A Student’s Suggestion: Video game theory lecture Open Yale Economics Ben Pollack’s Game Theory Lectures.

UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Bargaining and Negotiation Review.

QR 38, 2/22/07 Strategic form: dominant strategies I.Strategic form II.Finding Nash equilibria III.Strategic form games in IR.

Working Some Problems. Problem 3.10 Students 1 and 2 can each exert study levels {1,2,3,4,5}. Student 1’s exam score will be X+1.5 with effort level x.

EC941 - Game Theory Francesco Squintani Lecture 3 1.

UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Bargaining and Negotiation Review.

UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Bargaining and Negotiation Review.

Chapter 12 Choices Involving Strategy Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written.

“Life must be understood backward, but … it must be lived forward.”

Dominant strategies. Clicker Question 1, 3 5, 3 2, 4 7, 2 Player 2 Strategy A Strategy B Player 1 Strategy A Strategy B A ) Strategy A strictly dominates.

Dynamic Games of complete information: Backward Induction and Subgame perfection - Repeated Games -

Strategic Decisions in Noncooperative Games Introduction to Game Theory.

Game Theory: introduction and applications to computer networks Game Theory: introduction and applications to computer networks Lecture 2: two-person non.

Chapters 29, 30 Game Theory A good time to talk about game theory since we have actually seen some types of equilibria last time. Game theory is concerned.

3.1.4 Types of Games. Strategic Behavior in Business and Econ Outline 3.1. What is a Game ? The elements of a Game The Rules of the Game:

Introduction to Game Theory Economics 171. Course requirements Class website Go to economics department home page. Under Links, find Class pages, then.

Lecture 5 Introduction to Game theory. What is game theory? Game theory studies situations where players have strategic interactions; the payoff that.

1 What is Game Theory About? r Analysis of situations where conflict of interests is present r Goal is to prescribe how conflicts can be resolved 2 2 r.

Strategic Behavior in Business and Econ Static Games of complete information: Dominant Strategies and Nash Equilibrium in pure and mixed strategies.

Subgames and Credible Threats (with perfect information) Econ 171.

Subgames and Credible Threats

Subgames and Credible Threats. Nuclear threat USSR Don’t Invade Hungary 0101 Invade US Give in Bomb USSR

Game Theory (Microeconomic Theory (IV)) Instructor: Yongqin Wang School of Economics, Fudan University December, 2004.

Introduction to Game Theory Economics 171. Course requirements Class website Go to economics department home page. Under Links, find Class pages, then.

M9302 Mathematical Models in Economics Instructor: Georgi Burlakov 0.Game Theory – Brief Introduction Lecture

Subgames and Credible Threats. Russian Tanks Quell Hungarian Revolution of 1956.

ECO290E: Game Theory Lecture 3 Why and How is Nash Equilibrium Reached?

Choose one of the numbers below. You will get 1 point if your number is the closest number to 3/4 of the average of the numbers chosen by all class members,

Game Theory.  The analysis of situations in which players are interdependent.  Or…from the book….  a method of modelling the strategic interaction.

Taking Turns in the Dark: (Subgame perfection with incomplete information ) Econ 171.

Econ 805 Advanced Micro Theory 1 Dan Quint Fall 2009 Lecture 1 A Quick Review of Game Theory and, in particular, Bayesian Games.

By: Donté Howell Game Theory in Sports. What is Game Theory? It is a tool used to analyze strategic behavior and trying to maximize his/her payoff of.

Advanced Subjects in GT Outline of the tutorials Static Games of Complete Information Introduction to games Normal-form (strategic-form) representation.

Game theory basics A Game describes situations of strategic interaction, where the payoff for one agent depends on its own actions as well as on the actions.

Check your (Mis)understanding?

Game Theory: Day 6 What is Free Will?.

Presentation transcript:

Dominant strategies Econ 171

Clicker Question 1, 3 5, 3 2, 4 7, 2 Player 2 Strategy A Strategy B Player 1 Strategy A Strategy B A ) Strategy A strictly dominates Strategy B for both Players. B) Strategy B strictly dominates A for Player 1. Strategy A weakly dominates B for Player 2. C) Strategy B strictly dominates A for Player 1. Strategy A strictly dominates B for Player 2. D) Strategy B strictly dominates Strategy A for both players. E) No strategy in this game is strictly dominated

Strict and Weak Dominance Strategy A strictly dominates strategy B for a player if that player gets a higher payoff from doing A than from doing B no matter what the other player(s) do. Strategy A weakly dominates strategy B for a player gives at least as high a payoff no matter what the other player(s) do and for some actions of the others gives a higher payoff.

Game Theory Doctrine (A tautology) A rational player who understands the payoffs of a game and who tries to maximize his own payoff will A)never use a strictly dominated strategy. B)will always use a strictly dominant strategy if one exists.

Dominant strategies? 1 0, 10 0, , 0 1, 1 Strategy A Strategy B Player 1 Player 2 Does either strategy strictly dominate the other for Player 1? Does either strategy strictly dominate the other for Player 2? What is the predicted outcome? What are games like this called?

How about this one? 1 0, 10 0, , 0 1, 1 Strategy A Strategy B Player 1 Player 2 Does either strategy strictly dominate the other for Player 1? Does either strategy weakly dominate the other for Player 1? How about player 2? How would you play? Why?

Rousseau’s Stag Hunt 2, 2 0, 1 1, 0 1, 1 Stag Hare Player 1 Player 2 Are any strategies weakly dominated? Are any strategies strictly dominated? How would you play?

Gaming Pigs (Iterated dominance) Are there dominated strategies for Big Pig? How about Little Pig? How would you “solve” this game?

What went on in the pigpen

Kidnapping with imperfect information

Strategic Form

Kidnapping with Perfect Information

Kidnapping with complete information Pay RansomDon’t Pay Ransom Kidnap-- Kill if R, Kill if NR4,12,2 Kidnap—Release if R, Kill if NR5,32,2 Kidnap— Kill if R, Release if NR4,11,4 Kidnap—Release if R, Release if NR5,31,4 Don’t Kidnap– Kill, Kill3,5 Don’t Kidnap—Release, Kill3,5 Don’t kidnap--Kill, Release3,5 Don’t kidnap—Release, release3,5 Vivica Guy Are any strategies dominated for either player?

Clicker Question A) No strategies are strictly dominated for Player 1. Strategy w is dominated for Player 2 B ) No strategies are strictly dominated for either player. C) Strategy c is strictly dominated for Player 1. Strategies w and x are strictly dominated for Player 2. D) Strategy d is strictly dominated for Player 1. Strategies x and y are Strictly dominated for Player 2. E) No strategies are strictly dominated for Player 1. Strategies x and y are Strictly dominated for Player 2.

Iterated elimination and Common Knowledge Strategy a dominates c for Player 1. Strategy y dominates w and x for Player 2. Rational players won’t use these strategies. If each knows other is rational, then Player 2 know s that 1 won’t play c and 1 knows that 2 won’t play w or x. If both are rational and believe other is rational, Player 1 knows that 2 won’t play x or y, so Player 1 can eliminate b. Player 2 knows that Player 1 won’t play c, so Player 2 can eliminate y. If Player 1 knows that Player 2 knows that Player 1 is rational, then Player 1 knows Player 2 will Play z. What will Player 1 do?

Does Player 1 have a dominated strategy? Hint: Compare b and d.

Does Player 2 have a dominated strategy? Hint: Compare y and z.

If each knows the other won’t play a dominated strategy, we have a smaller game.

Reduced Game after one iteration. This is the game if each knows that the other is rational and each knows that the other knows that the other is rational. Are there any dominated strategies?

Reduced Game after 2 rounds of iterated elimination of strictly dominated strategies.

Reduced Game after 3 rounds of iterated elimination. Are there any strictly dominated strategies in this game? We have eliminated 12 of 16 strategies, but to get any further, We’re going to need more tools.