# STRATEGY AN INTRODUCTION TO GAME THEORY PDF

strategy third edition joel watson strategy an introduction to game theory joel watson university of california, san diego third edition myavr.info Strategy: An Introduction to Game Theory Second Edition Instructors' Manual Joel Watson with Jesse Bull April 1 Strategy: An Introduction to Game Theory. Joel Watson is Professor of Economics at the University of California, San Diego. He received his BA from UCSD and his PhD from Stanford. Watson is one of.

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Mar 5, 𝗣𝗗𝗙 | Sound managerial decision making often requires “putting yourself behind An Introduction to Game Theory and Business Strategy. Jul 20, The perfect balance of readability and formalism. Joel Watson has refined his successful text to make it even more student-friendly. A number of. Also by John C. Maxwell.. of the evening, as Steve and I were walking to our car, he said to me, “John, I bet That GAMES AND INFORMATION, THIRD.

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A number of sections have been added, and numerous chapters have been substantially revised.. Dozens of new exercises have been added, along with solutions to selected exercises. Chapters are short and focused, with just the right amount of mathematical content and end-of-chapter exercises.

New passages walk students through tricky topics. Download or read Aqualeo's The Book of Strategy: Very simple versions of the models are described and the equilibria of four of the examples are calculated.

Calculations for the other two models are left as exercises. Other equilibrium models can also be presented, either in addition to or substituting for the ones in the textbook. In each case, it may be helpful to organize the lecture as follows. Also, any of the applications can be used for classroom experiments.

Here is a game that can be played by e-mail, which may be useful in introducing mixed strategy Nash equilibrium in the next lecture. For example, if ten students picked 3, eight students picked 6, eleven students picked 7, and six students picked 8, then the mode is 7. If there are two or more modes, the highest is chosen. Let x denote the mode. The Nash equilibrium existence result is presented.

Lecture Notes Few applications and concepts rely on the analysis of mixed strategies, so the book does not dwell on the concept. However, it is still an important topic and one can present several interesting examples.

Here is a lecture outline. Ask for suggestions on how to play. Attack and defend. Discuss how some tactical choices in war can be analyzed using matching pennies-type games. Use a recent example or a historical exam- ple, such as the choice between Normandy and the Pas de Calais for the D-Day invasion of June 6, In the D-Day example, the Allies had to decide at which location to invade, while the Germans had to choose where to bolster their defenses.

A socially repeated strictly competitive game. This classroom experiment demon- strates how mixed strategies may be interpreted as frequencies in a population of players. The experiment can be done over the Internet or in class. The classroom version may be unwieldy if there are many students. The game can be played for money or for points in the class competition. Use a game that has a unique, mixed-strategy Nash equilibrium. Tell the students that some of them will be randomly selected to play this game against one another.

Ask all of the students to select strategies by writing them on slips of paper or using cards as described below. Compute the distribution of strategies for the entire class and report this to all of the students.

If the class frequencies match the Nash equilibrium, then discuss this. Otherwise, repeat the gaming procedure several times and discuss whether play converges to the Nash equilibrium.

Here is an idea for how to play the game quickly. At your signal, the students open their eyes. You can quickly calculate the strategy distribution and randomly select students from a class list to pay. Another version of the socially repeated game. Instead of having the entire class play the game in each round, have only two randomly selected students play.

In addition to demonstrating how random play can be interpreted and form a Nash equilibrium, the social repetition experiments also make the students familiar with strictly competitive games, which provides a good transition to the material in Chapter The chapter presents a result that is used in Chapter 17 for the analysis of parlor games. Lecture Notes One can present this material very quickly in class, or leave it for students to read.

An outline for a lecture may run as follows. Examples and Experiments Any abstract examples will do for a lecture. Much emphasis is placed on how con- tracts help to align beliefs and behavior in static settings. The discussion then shifts to settings of limited liability and default damage remedies. Self-enforced and externally enforced components. Explain why contracts are fundamental to economic relationships.

Default damage rules: Contract game. A contract game of the type analyzed in this chapter can be played as a classroom experiment.

You play the role of the external enforcer. Case study: Chicago Coliseum Club v. Dempsey Source: Facts of the Case: Dempsey was to engage in a boxing match with Harry Wills, another well- known boxer. However, he was never paid.

The Chicago Coliseum Club hired a promoter. When it contacted Dempsey con- cerning the life insurance, Dempsey repudiated the contract with the following telegram message. Clements President Chicago Coliseum Club Chgo Entirely too busy training for my coming Tunney match to waste time on insurance representatives stop as you have no contract suggest you stop kidding yourself and me also Jack Dempsey. Cases and Doctrine, 2d Ed.

Aspen , p. Expenses incurred after the signing of the agreement and before the breach of July 10, However, the court was not convinced of this as there were too many undetermined factors.

Unless shown otherwise, the court will generally assume that the venture would have at least broken even. The expenses incurred before the contract was signed with Dempsey could not be recovered as damages. Further, expenses incurred in relation to 3 above could only be recovered as damages if they occured before the repudiation.

The expense of 4 above could be recovered. Stylized Example The following technology of the relationship shows a possible interpretation when proof of the expected revenues is available. The concepts of perfect recall and perfect information are registered. Lecture Notes This material can be covered very quickly in class, as a transition from normal form analysis to extensive form analysis.

Here is an outline for a lecture. Forgetful driver. This one-player game demonstrates imperfect recall. The player reaches an intersection, where he must turn left or right. When he has to make a decision, the player does not recall how many intersections he passed through or what decisions he made previously. The extensive form representation is pictured on the next page. The notion of sequential rationality is presented, followed by backward induction a version of conditional dominance and then a demonstration of backward induction in an example.

Lecture Notes An outline for a lecture follows. Note that the entire game is itself a subgame. Incredible threats example. Grab game. This is a good game to run as a classroom experiment immediately after lecturing on the topic of subgame perfection. There is a very good chance that the two students who play the game will not behave according to backward induction theory. In this game, two students take turns on the move. When on the move, a student can either grab all of the money in your hand or pass.

If player 1 grabs the dollar, then the game ends player 1 gets the dollar and player 2 gets nothing. If player 2 passes, then you add another dollar and return to player 1. When it is known that each of a class of sub- games has a unique Nash equilibrium, one can identify the equilibrium and, treating it as the outcome induced by the subgame, work backward to analyze the game tree. Other equilibrium models, such as the von Stackelberg model, can also be presented or substituted for any in the chapter.

With regard to the advertising and limit capacity models as well as with others, such as the von Stackelberg game , the lecture can proceed as follows.

The dynamic monopoly game can be analyzed similarly, except it pays to stress intuition, rather than mathematical expressions, with this game. A result is stated for games that end with a winner and a loser or a tie. Thus, these games have pure strategy Nash equilibria and the equilibrium strategies are security strategies. If the game ends with either a winner or a tie, then either one of the players has a strategy that guarantees victory or both players can guarantee at least a tie.

Chomp tournament. Chomp is a fun game to play in a tournament format, with the students separated into teams. For the rules of Chomp, see Exercise 5 in Chapter Have the students meet with their team members outside of class to discuss how to play the game. The teams can then play against each other at the end of a few class sessions. After some thought after perhaps several days , the students will ascertain a winning strategy for the symmetric version of Chomp.

An optimal strategy for the asymmetric version will elude them, as it has eluded the experts.

Another tournament or challenge. The students might enjoy, and learn from, playing other parlor games between themselves or with you. An after-class challenge provides a good context for meeting with students in a relaxed envi- ronment. The chapter commences by noting how bargaining can be put in terms of value creation and division.

Several elements of negotiation—terms of trade, divisible goods—are noted. This representation is common in the cooperative game literature, where solution concepts are often expressed as axioms governing joint behavior. Transferable utility is assumed. Value creation means a higher joint value than with the disagreement point.

Descriptive and predictive interpretations. Negotiation experiments. It can be instructive—especially before lecturing on negotiation problems—to present a real negotiation problem to two or more students. Give them a set of alternatives such as transferring money, getting money or other objects from you, and so on. For example, one alternative might be that you will take student 1 to lunch at the faculty club, whereas another might be that you will give one of them their choice a new jazz compact disc.

You can have the students negotiate outside of class in a completely unstructured way although it may be useful to ask the students to keep track of how they reached a decision. Anonymous ultimatum bargaining experiment. Each should write a strategy on a slip of paper. This provides a good introduction to the theory covered in Chapter At the end of the chapter is an example of multilateral bargaining in the legislative context. Lecture Notes A lecture can proceed as follows.

Note that this observation will be used in larger games later. Bargaining weight interpretation of the outcome. De- termining the subgame perfect equilibrium using backward induction and the equilibrium of the ultimatum game. Sketch of the analysis: Convergence as discount factors approach one. This combines the negotiation experiment described in the material for Chapter 18 with the contract experiment in the material for Chapter A joint decision node is a distilled model of negotiation between the players; it takes the place of a noncooperative model of bargaining.

Games with joint decision nodes can be used to study complicated strategic settings that have a negotiation compo- nent, where a full noncooperative model would be unwieldy.

Behavior at joint decision nodes is characterized by the standard bargaining solution. Thus, a game with joint decision nodes is a hybrid representation, with cooperative and noncooperative components. The concept of a negotiation equilibrium combines sequential rationality at individual decision nodes with the standard bargaining solution at joint decision nodes. The chapter illustrates the ideas with an example of an incentive contract. Lecture Notes Here is an outline for a lecture.

In many strategic settings, negotiation is just one of the key compo- nents. Recall the pictures and notation from Chapter Tree Rule 6. Then, using the standard bargaining solution, determine the optimal contract and how the surplus will be divided.

Agency incentive contracting. You can run a classroom experiment where three students interact as follows. Students 1 and 2 have to play a matrix game. The contract between students 1 and 3 which you enforce can specify transfers between them as a function of the matrix game outcome. You can arrange the experiment so that the identities of students 1 and 3 are not known to student 2 by, say, allowing many pairs of students to write contracts and then selecting a pair randomly and anonymously, and by paying them privately.

After the experiment, discuss why you might expect t, rather than s, to be played in the matrix game. Ocean liner shipping-contract example. A producer who wishes to ship a moder- ate shipment of output say three or four full containers overseas has a choice of three ways of shipping the product. He can contract directly with the shipper, he can contract with an independent shipping contractor who has a contract with a shipper , or he can use a trade association that has a contract with a shipper.

Shipping the product is worth to the producer. Suppose that the producer only has time to negotiate with one of the parties because his product is perishable, but in the event of no agreement he can use the trade association.

An example is developed in which one of the players must choose whether to invest prior to production taking place. In the second version, parties can contract up front; here, option contracts are shown to provide optimal incentives.

The chapter also comments on how asset ownership can help alleviate the hold up problem.

Related to externality. Then determine the rational investment choice. Describe how option con- tracts work and are enforced. Calculate and describe the negotiation equilibrium. This may not be true in general. If the outside asset value rises too quickly with the investment, then the investor may have the incentive to overinvest. You can also present the analysis of, or run an experiment based on, a game like that of the Guided Exercise in this chapter.

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. Thus, the equilibria of the subgames are the same as those of the stage game. Grim trigger. The folk theorem.

## Strategy: An Introduction to Game Theory

Two-period example. 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.

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.

This example reinforces the basic analytical exercise from Chapter 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. 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. The Princess Bride second reputation example. While in the swamp, Wesley explains how a reputation can be associated with a name, even if the name changes hands over time.

Repeated Cournot oligopoly experiment. Let three students interact in a re- peated Cournot oligopoly.

## Game theory

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.

Another abstract example follows. Private information about preferences: For example, the buyer knows his own valuation of the good, which the seller does not observe. Nature moves at chance nodes, which are represented as open circles. In the incomplete-information 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.

This game also makes a good example see Exercise 4 in Chapter 24 of the textbook. 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.

Signaling games. It may be worthwhile to describe a signaling game that you plan to analyze later in class. 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, 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, The players make their guesses sequentially.

Player 3 next chooses a number, followed by player 4. After the players make their guesses, the actual price is revealed. The other players get 0. The bonus question is: 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. An example helps explain the notions of risk aversion and risk premia.

Then a streamlined principal-agent model is developed and fully analyzed. 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. Concavity, linearity, etc. Risk neutral principal. Discuss risk aversion and risk premia. Two methods are presented. The two methods are equivalent whenever all types are realized with positive probability an innocuous assumption for static settings.

The second method is shown to be useful when there are continuous strategy spaces, as illustrated using the Cournot duopoly with incomplete information. Examples and Experiments You can run a common- or private-value auction experiment or a lemons experi- ment in class as a transition to the material in Chapter You might also consider simple examples to illustrate the method of calculating best responses for individual player-types. 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 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. 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 c double integration to establish revenue equivalence.

One can skip c with no problem. Note whether the equilibrium is unique. 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. Tell them that whomever has the card in the end will get paid. If student 1 has the card, then she gets the amount written on it. 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- tion, or run any other type of auction in class. 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. A simple signaling game will do. Initial belief about types; updated posterior belief.

Note that conditional beliefs are unconstrained at zero-probability information sets. Conditional probability demonstration. 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.

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. 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. This game can be diagrammed and discussed in class. Exercise 6 in this chapter sketches one model of this strategic setting. The repu- tation model illustrates how incomplete information causes a player of one type to pretend to be another type, which has interesting implications. The extensive form tree of the job-market signaling model is in the standard signaling-game format, so this model can be easily presented in class.

Examples and Experiments In addition to, or in place of, the applications presented in this chapter, you might lecture on the problem of contracting with adverse selection.

Exercise 9 of Chapter 29 would be suitable as the basis for such a lecture.

Your students can con- sult this appendix to brush up on the mathematics skills that are required for game theoretic analysis. As noted at the beginning of this manual, calculus is used spar- ingly in the textbook and it can be avoided.

Appendix B gives some of the details of the rationalizability construction. Three challenging mathematical exercises appear at the end of Appendix B. Although we worked diligently on these solutions, there are bound to be a few typos here and there. Please report any instances where you think you have found a substantial error.

The order does not matter as it is a simultaneous move game. Exercise 1: Exercise 4: A strat- egy for the manager must specify an action to be taken in every contin- gency. Player 2 has 4 strategies: Some possible extensive forms are shown below and on the next page. Matching Pennies: Battle of the Sexes: Pareto Coordination: X dominates Z.

So we can iteratively delete dom- inated strategies. U dominates D.

**Also read:**

*LEARN GAME PROGRAMMING WITH RUBY PDF*

When D is ruled out, R dominates C. The order does not matter because if a strategy is domi- nated not a best response relative to some set of strategies of the other player, then this strategy will also be dominated relative to a smaller set of strategies for the other player.

If s1 is rationalizable, then s2 is a best response to a strategy of player 1 that may rationally be played. Thus, player 2 can rationalize strategy s2. So player 10 has a single undominated strategy, 0.

Given this, we know a will be at most 9 if everyone except player 10 selects 9. We label the regions as shown below. Noticing the symmetry makes this easier.

It is easy to see that if the regions are divided in half between 5 and 6 that is distributed to each half. In any of these outcomes, each candidate receives the same number of votes. Each video is a full lecture usually between 40 and 60 minutes with good audio and video quality, and pitched at a non-technical audience.

Transcripts of each lecture are available. Licence: All Rights Reserved Jim Ratliff's graduate-level course in game theory Jim Ratliff, University of Arizona These are the extensive materials used in a course "taught to students in their second year of the economics PhD program at the University of Arizona during the period. It includes a simple interactive game in Javascript. Links at the top of the page take you to an interactive quiz on the topic and a game solver. It has been produced by Stefan Waner and Steven R.

Costenoble of Hofstra University. The course contains many case studies. Licence: Not known: assume All Rights Reserved Added: 18 Apr Probability and decision Paul Bartha, University of British Columbia At the foot of this page are extensive notes from 15 lectures by a philosopher on game theory and rational choice.

Topics include the Allais and Ellsburg paradoxes, criteria of rationality and evolutionary considerations. This link goes to the Archive. McCain presents nearly twenty sections of an introductory game theory textbook. The site uses frames so that the index page and a content page are always presented together. The examples of game theory applications include queuing, college applications and marriage vows. Thomas Lux speaks on how economic systems can be seen as evolutionary models, where agents interact with each other and a selection process favours the most successful.Discuss risk aversion and risk premia.

Calculate the subgame perfect equilib- rium of this game and report the equilibrium strategies. Player 2 observes x. Then describe what it means for a player to not know what another player did. Your name: Information, relevance, and social decision making: Some principles and results of decision-theoretic semantics.

The bonus question is: Economics Final Examination Prof.

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