# An Introduction To Game Theory Joel Watson Pdf Download

2This Instructors Manual has four parts. Part I contains somenotes on outlining andpreparing a game theory course that is basedon the textbook. Part II contains moredetailed (but not overblown)materials that are organized by textbook chapter. PartIII comprisessolutions to all of the exercises in the textbook. Part IV containssomesample examination questions.

## an introduction to game theory joel watson pdf download

Below is a sample ten-week course outline that is formed bytrimming some ofthe applications from the thirteen-week outline.This is the outline that I use for myquarter-length game theorycourse. I usually cover only one application from eachof Chapters8, 10, 16, 23, 27, and 29. I avoid some end-of-chapter advancedtopics,such as the innite-horizon alternating-oer bargaining game,I skip Chapter 25, and,depending on the pace of the course, Iselectively cover Chapters 18, 20, 27, 28, and 29.

My feeling is that using a little bit of calculus is a goodidea, even if calculus isnot a prerequisite for the game theorycourse. It takes only an hour or so to explainslope and thederivative and to give students the simple rule of thumb forcalculatingpartial derivatives of simple polynomials. Then one caneasily cover some of the mostinteresting and historically importantgame theory applications, such as the Cournotmodel andauctions.

This chapter introduces the concept of a game and encourages thereader to beginthinking about the formal analysis of strategicsituations. The chapter contains ashort history of game theory,followed by a description of non-cooperative theory(which the bookemphasizes), a discussion of the notion of contract and the relateduseof cooperative theory, and comments on the science and art ofapplied theoreticalwork. The chapter explains that the word gameshould be associated with anywell-dened strategic situation, notjust adversarial contests. Finally, the format andstyle of the bookare described.

This chapter introduces the basic components of the extensiveform in a non-technicalway. Students who learn about the extensiveform at the beginning of a course aremuch better able to grasp theconcept of a strategy than are students who are taughtthe normalform rst. Since strategy is perhaps the most important concept ingametheory, a good understanding of this concept makes a dramaticdierence in eachstudents ability to progress. The chapter avoidsthe technical details of the extensiveform representation in favorof emphasizing the basic components of games. Thetechnical detailsare covered in Chapter 14.

As noted already, introducing the extensive form representationat the beginning ofa course helps the students appreciate thenotion of a strategy. A student that doesnot understand the conceptof a complete contingent plan will fail to grasp thesophisticatedlogic of dynamic rationality that is so critical to much of gametheory.Chapter 3 starts with the formal denition of strategy,illustrated with some examples.The critical point is thatstrategies are more than just plans. A strategy prescribesan actionat every information set, even those that would not be reachedbecause ofactions taken at other information sets.

2. The centipede game (like the one in Figure 3.1(b) if thetextbook). As with thebargaining game, have some students writetheir strategies on paper and givethe strategies to other students,who will then play the game as their agents.Discuss mistakes as areason for specifying a complete contingent plan. Thendiscuss howstrategy specications helps us develop a theory about whyplayersmake particular decisions (looking ahead to what they woulddo at variousinformation sets).

Optional introduction: analysis of a game played in class. If a33 dominance-solvable game (such as the one suggested in the notesfor Chapter 4) was playedin class earlier, the game can be quicklyanalyzed to show the students what isto come.

This chapter presents two important applied models. Theapplications illustrate thepower of proper game theoreticreasoning, they demonstrate the art of construct-ing game theorymodels, and they guide the reader on how to calculate the setofrationalizable strategies. The location game is a nite (ninelocation) version ofHotellings well-known model. This game has aunique rationalizable strategy prole.The partnership game hasinnite strategy spaces, but it too has a unique rational-izablestrategy prole. Analysis of the partnership game coaches the readeron howto compute best responses for games with dierentiable payofunctions and contin-uous strategy spaces. The rationalizable setis determined as the limit of an innitesequence. The notion ofstrategic complementarity is briey discussed in the contextof thepartnership game.

This chapter provides a solid conceptual foundation for Nashequilibrium, based on(1) rationalizability and (2) strategiccertainty, where players beliefs and behaviorare coordinated sothere is some resolution of the second strategic tension.Strate-gic certainty is discussed as the product of various socialinstitutions. The chapterbegins with the concept of congruity, themathematical representation of some co-ordination between playersbeliefs and behavior. Nash equilibrium is dened as aweaklycongruous strategy prole, which captures the absence of strategicuncertainty(as a single strategy prole). Various examples arefurnished. Then the chapter ad-dresses the issue of coordinationand welfare, leading to a description of the thirdstrategictensionthe specter of inecient coordination. Finally, there is anaside onbehavioral game theory (experimental work).

This chapter oers a brief treatment of two concepts that playeda major role inthe early development of game theory: two-player,strictly competitive games andsecurity strategies. The chapterpresents a result that is used in Chapter 17 for theanalysis ofparlor games.

2. Grab game. This is a good game to run as a classroomexperiment immediatelyafter lecturing on the topic of subgameperfection. There is a very good chancethat the two students whoplay the game will not behave according to backwardinductiontheory. You can discuss why they behave dierently. In this game,twostudents take turns on the move. When on the move, a student caneithergrab all of the money in your hand or pass. At the beginningof the game, youplace one dollar in your hand and oer it to player1. If player 1 grabs thedollar, then the game ends (player 1 getsthe dollar and player 2 gets nothing).If player 1 passes, then youadd another dollar to your hand and oer the twodollars to player 2.If she grabs the money, then the game ends (she gets $2and player 1gets nothing). If player 2 passes, then you add another dollarandreturn to player 1. This process continues until either one ofthe players grabsthe money or player 2 passes when the pot is $21(in which case the game endswith both players obtainingnothing).

2. Anonymous ultimatum bargaining experiment. Let half of thestudents be theoerers and the other half responders. Each shouldwrite a strategy on a slipof paper. For the oerers, this is anamount to oer the other player. For aresponder, this may be anamount below which she wishes to reject the oer(or it could be arange of oers to be accepted). Once all of the slips havebeencollected, you can randomly match an oerer and responder. It maybeinteresting to do this twice, with the roles reversed for thesecond run, and totry the non-anonymous version with two studentsselected in advance (in whichcase, their payos will probably dierfrom those of the standard ultimatumformulation). Discuss why (orwhy not) the students behavior departs fromthe subgame perfectequilibrium. This provides a good introduction to thetheory coveredin Chapter 19.