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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 2 left gloves of different colors. How many different ways can Wilbur dress himself?. Iraq War Game. 1. 3. 2. - PowerPoint PPT Presentation

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The Random Dresser(Clicker Question) Wilbur has 3 left shoes, all of different colors5 right shoes, all of different colors4 right gloves, all of different colors 2 left gloves of different colors.How many different ways can Wilbur dress himself?A) 14 B) 28 C) 48 D) 120 E) 240 Monte Hall Problem

Lets Draw a Game Tree

Problem 6, chapter 2Information sets in Monte Hall gameIn last move, contestant knows which door he chose and which Monte opened. The door that Monte opened is neither the one that contestant opened nor the one with the good prize.Six things contestant might see.1/ 2, 1/ 3, 2/ 1, 2/ 3, 3/ 1, 3/ 2. To stay or to switch: that is the question.If your initial choice was right, then you win if you stay and lose if you switch. If your initial choice was wrong, you lose if you stay and you win if you switch.What is the probability that your initial choice was right? What is probability you win if you stay?What is probability you win if you switch?

Iraq War Game123What are the strategies for Saddam?For Saddam we have to say what he would do at each node where it is his turn. There are 3 nodes. We list actions at each node to specify a strategy:No WMD, Deny, DenyNo WMD, Deny, AllowNo WMD, Deny, Allow and HideNo WMD, Allow, DenyNo WMD, Allow, AllowNo WMD, Allow, Allow and HideWMD, Deny, DenyWMD, Deny, AllowWMD, Deny, Allow and HideWMD, Allow, DenyWMD, Allow, AllowWMD, Allow, Allow and Hide

What does that mean?How do we interpret a strategy like,No WMD, Allow, Deny?This means 1) he chooses to have no wmd, 2) if the UN asks to inspect and he has no wmd, he allows them to inspect 3) if the UN asks to inspect and he has wmd, he denies inspection.So, you ask, if he chooses no wmd, why do we need to specify what he will do at decision node 3?Imagine that Saddam commanded No WMD, but discovers that his orders werent followed and he realizes that he has WMD and the UN wants to inspect. What will he do?Game theory needs to deal with such possibilities.Dominant strategies

Clicker Question 1 , 3 5, 3 2, 4 7, 2Player 2Strategy AStrategy BPlayer 1Strategy AStrategy BA ) 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 dominatedStrict and Weak DominanceStrategy 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.Clicker Question 2,2 0, 3 3, 0 1,1Player 2Strategy AStrategy BPlayer 1Strategy AStrategy BA ) 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 Game Theory Doctrine (A tautology) A rational player who understands the payoffs of a game and who tries to maximize his own payoff will never use a strictly dominated strategy. will always use a strictly dominant strategy if one exists.Dominant strategies? 1 0 , 10 0, 11 1 1, 0 1, 1Strategy AStrategy A Strategy BStrategy BPlayer 1Player 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, 10 1 0, 0 1, 1Strategy AStrategy A Strategy BStrategy BPlayer 1Player 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?

Clicker Question 1 0 , 10 0, 10 1 0, 0 1, 1Strategy AStrategy A Strategy BStrategy BPlayer 1Player 2

If I were playing this game just once with a stranger whom I would never meet again, I would:Play Strategy APlay Strategy B

Rousseaus Stag Hunt 2 , 2 0 , 1 1 , 0 1 , 1StagStagHareHarePlayer 1Player 2

Are any strategies weakly dominated?

Are any strategies strictly dominated?How would you play?Clicker Question 2 , 2 0 , 1 1 , 0 1 , 1StagStagHareHarePlayer 1Player 2

If you were playing Rosseaus stag hunt with astranger, whom you will never meet again, which strategy would you play? A) Stag B) HareGaming 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

The Entry Game ChallengerStay out

0 Challengers payoff1 Incumbents payoffChallengeIncumbentGive in

Fight10-1 -1

Challengers payoffIncumbents payoffStrategic Form of Entry Game0,10,11,0-1,-1Give inFightStay outEnterChallengerIncumbent21Dominance in Entry Game?No dominant strategy for Challenger. Which is better depends on what incumbent will do.Give-in is weakly dominant for Incumbent.

If Challenger believes that Incumbent is rational, Challenger believes that Incumbent will give in. In this case, predicted outcome is Challenger enters and incumbent gives in. What if incumbent could precommit?

Could the incumbent make a credible threat to fight if challenger enters. If he could, he could get challenger to stay out. On blackboard we will draw a game that allows incumbent the choice of committing to to be badly punished if he gives in.Lets do this so that the solution is that the incumbent chooses to make this commitment and the challenger stays out.Tools for understanding this solution will arrivelater in this course.Kidnapping with imperfect information

Strategic Form

Dominated strategies?Guy doesnt have any dominated strategiesBut for Vivica, Dont Pay dominates Pay.What does iterated elimination of dominated strategies tell us?If Guy knows that Vivica is rational, he knows she wont pay ransom.If Guy knows that Vivica wont pay ransom, he is better off not kidnapping.Kidnapping with Perfect Information

Kidnapping with complete informationPay RansomDont Pay RansomKidnap-- Kill if R, Kill if NR4,12,2KidnapRelease if R, Kill if NR5,32,2Kidnap Kill if R, Release if NR4,11,4KidnapRelease if R, Release if NR5,31,4Dont Kidnap Kill, Kill3,53,5Dont KidnapRelease, Kill3,53,5Dont kidnap--Kill, Release3,53,5Dont kidnapRelease, release3,53,5VivicaGuy

Are any strategies strictly dominated for either player?Dominated strategies?Neither strategy dominates for VivicaFor Guy, KidnapRelease if Ransom, Kill if No ransom weakly dominates all other strategies that start with Kidnap.So if Vivica believe that Guy is rational, then she believes that if Guy Kidnaps, he will kill if no ransom and release if ransom.So Vivica would pay ransomSo Guy would Kidnap and release after receiving ransom.

Does Player 1 have a dominated strategy? Hint: Compare b and d.30

Does Player 2 have a dominated strategy? Hint: Compare y and z.Iterated Elimination of Dominated Strategies-Stage 131

If each knows the other wont play a dominated strategy, we have a smaller game.The game After first round of Eliminaton32

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?33

Reduced Game after 2 rounds of iterated elimination of strictly dominated strategies. (Note that x couldnt have been eliminated in the first round.)34

Reduced Game after 3 rounds of iterated elimination.a is eliminated. This couldnt have been done in earlier rounds.

Are there any strictly dominated strategies in this game?

We have eliminated 12 of 16 strategies, but to get any further,Were going to need more tools.35Iterated elimination and Common Knowledge

Strategy a dominates c for Player 1. Strategy y dominates w and x for Player 2. Rational players wont use these strategies. If each knows other is rational, then Player 2 know s that 1 wont play c and 1 knows that 2 wont play w or x.If both are rational and believe other is rational, Player 1 knows that 2 wont play x or y, so Player 1 can eliminate b. Player 2 knows that Player 1 wont play c, so Player 2 can eliminate y. If Player 1 knows that Player 2 knows that Player 1 is rational, thenPlayer 1 knows Player 2 will Play z. What will Player 1 do?

And Steer Clear of Dominated Strategies See you on Thursday

Clicker QuestionA) No strategies are strictly dominated for Player 1. Strategy w is dominated for Player 2B) 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 2.38