### Create a StudySoup account

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

Already have a StudySoup account? Login here

# SCENIC DESIGN THTR 22

UCSB

GPA 3.6

### View Full Document

## 42

## 0

## Popular in Course

## Popular in Theatre

This 14 page Class Notes was uploaded by Kobe Dare on Thursday October 22, 2015. The Class Notes belongs to THTR 22 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 42 views. For similar materials see /class/226864/thtr-22-university-of-california-santa-barbara in Theatre at University of California Santa Barbara.

## Reviews for SCENIC DESIGN

### 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: 10/22/15

22 Repeated Games and Reputation This chapter opens with comments about the importance of reputation in ongoing relationships The concept of a repeated game is de ned and a two period repeated game is analyzed in detail The two period game demonstrates that any sequence of stage Nash pro les can be supported as a subgame perfect equilibrium outcome a result that is stated for general repeated games The example also shows how a non stage Nash pro le can be played in equilibrium if subsequent play is conditioned so that players would be punished for deviating The chapter then turns to the analysis of in nitely repeated games beginning with a review of discounting The presenta tion includes derivation of the standard conditions under which cooperation can be sustained in the in nitely repeated prisoners7 dilemma In the following section a more complicated asymmetric equilibrium is constructed to demonstrate that differ ent forms of cooperation favoring one or the other player can also be supported A Nash punishment folk theorem is stated at the end of the chapter Lecture Notes A lecture may be organized according to the following outline o lntuition reputation and ongoing relationships Examples partnerships col lusion etc Key idea behavior is conditioned on the history of the relationship so that misdeeds are punished De nition of a repeated game Stage game A u call A actions played T times with observed actions 0 Example of a two period non discounted repeated game 0 Diagram of the feasible repeated game payoffs and feasible stage game payoffs 0 Note how many subgames there are Note what each playerls strategy speci es o The proper subgames have the same strategic features since the payoff matrices for these are equal up to a constant Thus the equilibria of the subgames are the same as those of the stage game 0 Characterization of subgame perfect equilibria featuring only stage Nash pro les action pro les that are equilibria of the stage game A reputation equilibrium where a non stage Nash action pro le is played in the rst period Note the payoff vector 0 Review of discounting Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 22 REPEAT ED GAMES AND REP UTAT I ON 57 o The in nitely repeated prisoners7 dilemma game 0 Trigger strategies Grim trigger 0 Conditions under which the grim trigger is a subgame perfect equilibrium 0 Example of another cooperative equilibrium The folk theorem Examples and Experiments 1 Two period example It is probably best to start a lecture with the simplest possible example such as the one with a 3 x 2 stage game that is presented at the beginning of this chapter You can also run a classroom experiment based on such a game Have the students communicate in advance either in pairs or as a group to agree on how they will play the game That is have the students make a self enforced contract This will hopefully get them thinking about history dependent strategies Plus it will reinforce the interpretation of equilibrium as a self enforced contract which you may want to discuss near the end of a lecture on reputation and repeated games E0 The Princess Bride reputation example At the beginning of your lecture on reputation you can play the scene from The Princess Bride in which Wesley is reunited with the princess Just before he reveals his identity to her he makes interesting comments about how a pirate maintains his reputation Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 23 Collusion Trade Agreements and Goodwill This chapter presents three applications of repeated game theory collusion between rms over time the enforcement of international trade agreements and goodwill The rst application involves a straightforward calculation of whether collusion can be sustained using grim trigger strategies in a repeated Cournot model This example reinforces the basic analytical exercise from Chapter 22 The section on international trade is a short verbal discussion of how reputation functions as the mechanism for self enforcement of a long term contract On goodwill a two period game with a sequence of players 2 one in the rst period and another in the second period is analyzed The rst player 2 can by cooperating in the rst period establish a valuable reputation that he can then sell to the second player 2 Lecture Notes Any or all of the applications can be discussed in class depending on time con straints and the students7 background and interest Other applications can also be presented in addition to these or substituting for these For each application it may be helpful to organize the lecture as follows 0 Description of the real world setting 0 Explanation of how some key strategic elements can be distilled in a game theory model o If applicable Description of the game to be analyzed 0 Determination of conditions under which an interesting cooperative equilib rium exists 0 Discussion of intuition 0 Notes on how the model could be extended Examples and Experiments 1 The Princess Bride second reputation example Before lecturing on goodwill you can play the scene from The Princess Bride where Wesley and Buttercup are in the re swamp While in the swamp Wesley explains how a reputation can be associated with a name even if the name changes hands over time lnstructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute COLLUSION TRADE AGREEMENTS AND GOODWILL 59 2 Goodwill in an in nitely repeated game If you want to be ambitious you can present a model of an in nitely repeated game with a sequence of players 2 who buy and sell the player 2 reputation77 between periods This can follow the Princess Bride scene and be based on Exercise 4 of this chapter which depending on your students7 backgrounds may be too dif cult for them to do on their own 9 Repeated Coumot oligopoly experiment Let three students interact in a re peated Cournot oligopoly This may be set as an oil or some other commodity production game It may be useful to have the game end probabilistically This may easy to do if it is done by e mail but may require a set time frame if done in class The interaction can be done in two scenarios In the rst players may not communicate and only the total output is announced at the end of each round In the second scenario players are allowed to communicate and each playerls output is announced at the end of each round lnstructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 24 Random Events and Incomplete Information This chapter explains how to incorporate exogenous random events in the speci cation of a game Moves of Nature also called the nonstrategic player 0 are made at chance nodes according to a xed probability distribution As an illustration the gift game is depicted in the extensive form and then converted into the Bayesian normal form where payoffs are the expected values over Nature7s moves Another abstract example follows Lecture Notes A lecture may be organized according to the following outline 0 Discussion of settings in which players have private information about strategic aspects beyond their physical actions Private information about preferences auctions negotiation etc 0 Modeling such a setting using moves of Nature that players privately observe For example the buyer knows his own valuation of the good which the seller does not observe Extensive form representation of the example Nature moves at chance nodes which are represented as open circles Nature7s probability distribution is noted in the tree 0 The notion of a type referring to the information that a player privately ob serves lf a player privately observes some aspect of Nature7s choices then the game is said to be of incomplete information Many real settings might be described in terms of players already knowing their own types However because of incomplete information one type of player will have to consider how he would have behaved were he a different type because the other players consider this 0 Bayesian normal form representation of the example Note that payoff vectors are averaged with respect to Nature7s xed probability distribution 0 Other examples lnstructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute RANDOM EVENTS AND INCOMPLETE INFORMATION 61 Examples and Experiments 1 The Let s Make a Dealgame revisited You can illustrate incomplete information by describing a variation of the Lets Make a Deal game that is described in the material for Chapter 2 In the incompleteinformation version Nature picks with equal probabilities the door behind which the prize is concealed and Monty randomizes equally between alternatives when he has to open one of the doors 3 Three card poker This game also makes a good example see Exercise 4 in Chapter 24 of the textbook CA3 Ultimatum o er bargaining with incomplete information You might present or run as a classroom experiment an ultimatum bargaining game in which the responders value of the good being traded is private information say 5 with probability 12 and 8 with probability 12 For an experiment describe the good as a soon expiring check made out to player 2 You show player 2 the amount of the check but you seal the check in an envelop before giving it to player 1 who bargains over the terms of trading it to player 2 gt Signaling games It may be worthwhile to describe a signaling game that you plan to analyze later in class U The Price is Right The bidding game from this popular television game show forms the basis for a good bonus question See also Exercise 5 in Chapter 25 for a simpler but still challenging version In the game four contestants must guess the price of an item Suppose none of them knows the price of the item initially but they all know that the price is an integer between 1 and 1 000 In fact when they have to make their guesses the contestants all believe that the price is equally likely to be any number between 1 and 1 000 That is the price will be 1 with probability 11000 the price will be 2 with probability 11000 and so on The players make their guesses sequentially First player 1 declares hisher guess of the price by picking a number between 1 and 1 000 The other players observe player 17s choice and then player 2 makes her guess Player 3 next chooses a number followed by player 4 When a player selects a number heshe is not allowed to pick a number that one of the other players already had selected After the players make their guesses the actual price is revealed Then the player whose guess is closest to the actual price without going over wins 100 The other players get 0 For example if player 1 chose 150 player 2 chose 300 player 3 selected 410 and player 4 chose 490 and if the actual price were 480 then player 3 wins 100 and the others get nothing Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute RANDOM EVENTS AND INCOMPLETE INFORMATION 62 This game is not exactly the one played on The Price is Right7 but it is close The bonus question is Assuming that a subgame perfect equilibrium is played7 what is player 17s guess How would the answer change if7 instead of the winner getting 1007 the winner gets the value of the item that is7 the actual price Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 25 Risk and Incentives in Contracting This chapter presents the analysis of the classic principal agent problem under moral hazard where the agent is risk averse There is a move of Nature a random produc tive outcome Because Nature moves last the game has complete information Thus it can be analyzed using subgame perfect equilibrium This is why the principal agent model is the rst and most straightforward application covered in Part IV of the book At the beginning of the chapter the reader will nd a thorough presentation of how payoff numbers represent preferences over risk An example helps explain the notions of risk aversion and risk premia The Arrow Pratt measure of relative risk aversion is de ned Then a streamlined principal agent model is developed and fully analyzed The relation between the agents risk attitude and the optimal bonus contract is determined Lecture Notes Analysis of the principal agent problem is fairly complicated Instructors will not likely want to develop in class a more general and complicated model than the one in the textbook A lecture based on the textbooks model can proceed as follows 0 Example of a lottery experiment questionnaire that is designed to determine the risk preferences of an individual 0 Representing the example as a simple game with Nature Note that people usually are risk averse in the sense that they prefer the ex pected value of a lottery over the lottery itself Observe the difference between an expected monetary award and expected util ity payoff Risk preferences and the shape of the utility function on money Concavity linearity etc o Arrow Pratt measure of relative risk aversion o lntuition contracting for effort incentives under risk 0 The principal agent model Risk neutral principal o Incentive compatibility and participation constraints They both will bind at the principals optimal contract offer 0 Calculation of the equilibrium Note how the contract and the agents behavior depend on the agents risk preferences 63 Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 25 RISK AND INCENTIVES IN CONTRACTING 64 0 Discussion of real implications Examples and Experiments You can illustrate risk aversion by offering Choices over real lotteries to the stu dents in Class Discuss risk aversion and risk premia Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 26 Bayesian Nash Equilibrium and Rationalizability This chapter shows how to analyze Bayesian normal form games using rationalizability and equilibrium theory Two methods are presented The rst method is simply to apply the standard de nitions of rationalizability and Nash equilibrium to Bayesian normal forms The second method is to apply the concepts by treating different types of a player as separate players The two methods are equivalent whenever all types are realized with positive probability an innocuous assumption for static settings Computations for some nite games exemplify the rst method The second method is shown to be useful when there are continuous strategy spaces7 as illustrated using the Cournot duopoly with incomplete information Lecture Notes A lecture may be organized according to the following outline 0 Examples of performing standard rationalizability and equilibrium analysis to Bayesian normal form games 0 Another method that is useful for more complicated games such as those with continuous strategy spaces treat different types as different players One can use this method without having to calculate expected payoffs over Nature7s moves for all players 0 Example of the second method Cournot duopoly with incomplete information or a different game Examples and Experiments You can run a common or privatevalue auction experiment or a lemons experi ment in class as a transition to the material in Chapter 27 You might also consider simple examples to illustrate the method of calculating best responses for individual player types Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 27 Lemons Auctions and Information Aggregation This chapter focuses on three important settings of incomplete information price taking market interaction auctions and information aggregation through voting These settings are studied using static models in the Bayesian normal form and the games are analyzed using the techniques discussed in the preceding chapter The markets and lemons77 game demonstrates Akerlofls major contribution to informa tion economics Regarding auctions the chapter presents the analysis of both rst price and second price formats In the process weak dominance is de ned and the revenue equivalence result is mentioned The example of voting and information aggregation gives a hint of standard mechanism designsocial choice analysis and il lustrates Bayes7 rule Lecture Notes Any or all of these applications can be discussed in class depending on time constraints and the students7 background and interest The lemons model is quite simple a lemons model that is more general than the one in the textbook can easily be covered in class The auction analysis on the other hand is more complicated However the simpli ed auction models are not beyond the reach of most advanced undergraduates The major sticking points are a explaining the method of assuming a parameterized form of the equilibrium strategies and then calculating best responses to verify the form and determine the parameter b the calculus required to calculate best responses and 0 double integration to establish revenue equivalence One can skip c with no problem The information aggregation example requires students to work through Bayes7 rule calculations For each application it may be helpful to organize the lecture as follows 0 Description of the real world setting 0 Explanation of how some key strategic elements can be distilled in a game theory model 0 Description of the game to be analyzed 0 Calculations of best responses and equilibrium Note whether the equilibrium is unique 0 Discussion of intuition 0 Notes on how the model could be extended Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute LEMONS AUCTIONS AND INFORMATION AGGREGATION 67 Examples and Experiments 1 Lemons experiment Let one student be the seller of a car and another be the potential buyer Prepare some cards with values written on them Show the cards to both of the students and then7 after shuf ing the cards7 draw one at random and give it to student 1 so that student 1 sees the value but student 2 does not Let the students engage in unstructured negotiation over the terms of trading the card from student 1 to student 27 or allow them to declare whether they will trade at a prespeci ed price Tell them that whomever has the card in the end will get paid If student 1 has the card7 then she gets the amount written on it If student 2 has the card7 then he gets the amount plus a constant 2 perhaps E0 Stock trade and auction experiments You can run an experiment in which randomly selected students play a trading game like that of Exercise 8 in this chapter Have the students specify on paper the set of prices at which they are willing to trade You can also organize the interaction as a common value auc tion7 or run any other type of auction in class You can discuss the importance of expected payoffs contingent on winning or trading Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 28 Perfect Bayesian Equilibrium This chapter develops the concept of perfect Bayesian equilibrium for analyzing be havior in dynamic games of incomplete information The gift game is utilized through out the chapter to illustrate the key ideas First the example is used to demonstrate that subgame perfection does not adequately represent sequential rationality Then comes the notion of conditional belief which is presented as the belief of a player at an information set where he has observed the action but not the type of another player Sequential rationality is de ned as action choices that are optimal in response to the conditional beliefs for each information set The chapter then covers the notion of consistent beliefs and Bayes7 rule Finally perfect Bayesian equilibrium is de ned and put to work on the gift game Lecture Notes A lecture may be organized according to the following outline 0 Example to show that subgame perfection does not adequately capture sequen tial rationality A simple signaling game will do 0 Sequential rationality requires evaluating behavior at every information set Conditional belief at an information set regardless of whether players origi nally thought the information set would be reached Initial belief about types updated posterior belief o Sequential rationality optimal actions given beliefs like best response but with actions at a particular information set rather than full strategies 0 Consistency updating should be consistent with strategies and the basic de nition of conditional probability Bayes7 rule Note that conditional beliefs are unconstrained at zero probability information sets Perfect Bayesian equilibrium strategies beliefs at all information sets such that 1 each player7s strategy prescribes optimal actions at all of his information sets given his beliefs and the strategies of the other players and 2 the beliefs are consistent with Bayes7 rule wherever possible 0 De nition of pooling and separating equilibria Algorithm for nding perfect Bayesian equilibria in a signaling game a posit a strategy for player 1 either pooling or separating b calculate restrictions on conditional beliefs 0 calculate optimal actions for player 2 given his beliefs and d check whether player 17s strategy is a best response to player 27s strategy 0 Calculations for the example Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 28 PERFECT BAYESIAN EQUILIBRIUM 69 Examples and Experiments 1 Conditional probability demonstration Students can be given cards with differ ent colors written on them say red and blue The colors should be given in different proportions to males and females for example males could be given proportionately more cards saying red and females could be given proportion ately more cards saying blue A student could be asked to guess the color of another student7s card This could be done several times and the color revealed following the guess Then a male and female student could be selected and a student could be asked to guess who has for example the red card E0 Signaling game experiment It may be instructive to play in class a signaling game in which one of the player types has a dominated strategy The variant of the gift game discussed at the beginning of Chapter 28 is such a game CA3 The Princess Bride signaling example A scene near the end of The Princess Bride movie is a good example of a signaling game The scene begins with Wesley lying in a bed The prince enters the room The prince does not know whether Wesley is strong or weak Wesley can choose whether or not to stand Finally the prince decides whether to ght or surrender This game can be diagrammed and discussed in class After specifying payoffs you can calculate the perfect Baysian equilibria and discuss whether it accurately describes events in the movie Exercise 6 in this chapter sketches one model of this strategic setting Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute

### 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

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "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!"

#### "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.