### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# GAMETHEORY ECON1200

Pitt

GPA 3.53

### View Full Document

## 37

## 0

## Popular in Course

## Popular in Economcs

This 14 page Class Notes was uploaded by Quentin Huel Jr. on Monday October 26, 2015. The Class Notes belongs to ECON1200 at University of Pittsburgh taught by JohnDuffyJr in Fall. Since its upload, it has received 37 views. For similar materials see /class/229425/econ1200-university-of-pittsburgh in Economcs at University of Pittsburgh.

## Popular in Economcs

## Reviews for GAMETHEORY

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/26/15

Complete vs Incomplete Information Games O All games can be classi ed as complete information games or incomplete information games complete information games the player whose turn it is to move knows at least as much as those who moved before himher Complete information games include I Perfect information games players know the full history of the game all moves made by all players etc and all payoffs e g an extensive form game without any information sets 0 Imperfect information games games involving simultaneous moves where players know all the possible outcomespayoffs but not the actions chosen bi other 1 la ers D Incomplete information games At some node in the game the player whose turn it is to make a choice knows less than a player who has already moved Also called Bayesian games Imperfect vs Incomplete Information Games In a Uame of iml erfect information 1 la ers are simply unaware of the actions chosen by other players However they know who the other players are what their poss1ble Strategiesactions are ano the preferencespayoffs of these other players Hence information about the other A la ers in imperfect information is complete In incomplete information games players may or may not know some information about the other players eg their type their strategies payoffs r hir1rfrn Example la of an Incomplete Information Game Prisoner s Dilemma Game Player 1 has the standard sel sh preferences but Player 2 has either sel sh preferences or nice preferences Player 2 knows her type but Player 1 does not um type C 2 D C 2 D 1 C 44 06 1 C 46 04 D 60 22 D 62 20 Player 2 selfish Player 2 nice Recall that Ccooperate Ddefect If player 2 is selfish then player 1 will want to choose D but if player 2 is nice player 1 s best response is still to choose D since D is a dominant strategy for player 1 in this incomplete information game Example lb of an Incomplete Information Game Prisoner s Dilemma Game Player 1 has the standard sel sh preferences but Player 2 has either sel sh preferences or nice preferences Suppose player 1 s preferences now depend on whether player 2 is nice or sel sh or Vice versa C D C D 1 C 44 06 1 C 66 24 D 60 22 D 42 00 Player 2 selfish Player 2 nice If 2 is selfish then player 1 will want to be selfish and choose D but if player 2 is nice player 1 s best response is to play C 39 56 HICCI39 39O UIOSC WHO play HICG mean 390 UIOSC WHO play mean Examl 1e 1b in Extensive Form Where Plaver 2 s TVDe is Due to Nature 7 7 Mmsenshpmn m nuance thm Infnrmaunn Set Prevents 1 mm Knnwmg 239 Type and 239 ane icyggumd anyelg e 9mm enapeme 7 i v nmm Cunpude my nemet Cnnpemlz i 4 7r 7 v v Example 1b Again But With a Higher Probability that Type 2 is Sel sh 23 semgh Plan 23 n MELT Wag Wag mama magi mm muf e T W 7W W W Anal sis of Exam le lb Player 2 knows his type and plays his dominant strategy D if sel sh C if nice Player l s choice depends on her expectation concerning the unknown type of player 2 If player 2 is sel sh player i s best response is to play D If player 2 is nice player l s best response is to play C Suppose player 1 attaches probability p to Player 2 being sel sh so Ip is the probability that Player 2 is nice Player l s expected payoff from C is Op61 p Pla er l s ex ected A a off from D is 2p41 p 0p6Ip 2p4Ip 66p42p 24p pl2 Player l s best response is to play C if pltl2 D otherwise In rst version pl3 play C in second p23 play D The Nature of Nature What does it mean to add nature as a player It is simply a proxy for saying there is some randomness in the type of player with whom you play a game The probabilities associated with nature s move are the subjective probabilities of the player facing the uncertainty about the other player s type When thinking about player types two stories can be told The identity of a player is known but his preferences are unknown 1 know I am playing against Tom but I do not know whether he is sel sh or nice Nature whispers to Tom his type and I the other player have to gure it out Nature selects from a population of potential player types I am going to play against another player but I do not know if she is smart or dumb forgiving or unforgiving rich or poor etc Nature decides Example 2 Michelle and the Two Faces of Jerry J J Dancing Frat Party Dancing Frat Party Dancing Dancing M 21 00 M 20 02 Frat Party 090 132 Frat Party 031 130 Jerry likes company Jerry is a loner Assume that Jerry knows his true type and therefore which of the two games are being played Assume Michelle attaches probability p to Jerry liking company and lp to Jerry being a loner Big assumption Assume Jerry knows Michelle s estimate of p assumption of a common prior 1I2 Likes Company Prob 1 gt 12 Is a Loner Prob 12 The Game in Extensive Form BayesNash Equilibria BayesNash equilibria is generalization of Nash equilibrium for an incomplete information game First convert the game into a game or imperfect information Second use the Nash equilibria of this imperfect information game as the solution concept Apply this technique to the Michelle and Jerry Game Michelle s pure strategy choices are Dancing D or Party P She can also play a mixed strategy D With probability L J erry s strategy is a pair one for each type of Jerry the rst component is for the Jerry Who likes company Jerry type 1 and the second component is for Jerry the loner Jerry type 2 Pure strategies for Jerry are thus DD DP PD and PP Jerry also has a pair of mixed strategies L1 and L2 indicating the probability Jerry plays D if type lor if type 2 Focus on pure strategies Pure Strategy BayesNash Equilibria Suppose Michelle plays D for certain 1 Type 1 Jerry plays D Type 2 Jerry plays P Jerry DP 21 Does Michelle maximize her payoffs by playing D against the Jerrys pure strategy of DP With probability p she gets the DD payoff 2 and with probability lp she gets the DP payoff 0 So expected payoff from D against Jerry DP is 2p If instead she played P against Jerry DP she would get with probability p the PD payoff 0 and with probability lp she gets the PP payoff 1 So expected payoff from P against Jerry DP is lp Thus playing D against Jerry DP is a best response if 2pgt1p or if 3p gt1 or if pgt13 If pgt13 it is a BayesNash equilibrium for Michelle to play D While the Jerrys play DP Pure Strategy BayesNash Equilibria Contd 7 El Next suppose Michelle plays P for certain 0 Type 1 Jerry plays P Type 2 Jerry plays D Jerry PD Q Does Michelle maximize her payoffs by playing P against the Jerrys pure strategy of PD With probability p she gets the PP payoff 1 and with probability lp she gets the PD payoff 0 So expected payoff from P against Jerry PD is p If she instead played D against Jerry PD she would get with probability p the DP payoff 0 and with probability lp she gets the DD payoff 2 So the expected payoff from D against Jerry PD is 21p Finally playing P against Jerry PD is a best response if p gt 2lp or if 3p gt2 or if p gt 23 If pgt23 it is a BayesNash equilibrium for Michelle to play P While the J err s A la PD

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.