Presentation on theme: "Games People Play Economics 327 – Professor Chris Ellis."— Presentation transcript:
Games People Play Economics 327 – Professor Chris Ellis
Games People Play. Games People Play: Some Preliminary Questions. Question: What is game theory? Answer: The analysis of strategic situations. Question: And what is a strategic situation? Answer: When two or more players follow strategies (plans of action) that effect each others payoffs (happiness, money, status etc) we have a strategic situation. Question: What can a course on game theory do for me? Answer: It will allow you to predict the likely outcome of any strategic situation, and possibly tell you how to manipulate the outcome to your advantage.
Games People Play. Games People Play Remark: Sure it will….give me an example. Reply: Remember Cortez, the guy that conquered the Aztec empire. He used an understanding of game theory to achieve victory. On landing on the shores of Mexico he found that he and his conquistadors were outnumbered hundreds to one by a waiting Aztec army. Faced by these odds his response was to burn his boats, giving his troops no avenue of retreat. Remark: Cortez was a nutter!! Reply: No, he understood game theory. After his action his troops knew they had to fight to the death and the Aztecs knew it too. So the Aztecs ran away. Remark: What’s that got to do with me and my degree? Reply: Well, the battle could be your efforts to get an A on this course, and you are Cortez. If you can find a way of denying yourself the ability to take time off from studying so as to drink beer you might achieve your objective. Remark: I didn't know Cortez was an undergrad!! Reply: Huh?!?!
Games People Play. Games People Play
Games People Play. Games People Play Syllabus Text: Dixit and Skeath, “Games of Strategy” 2 nd Edition, Norton. Useful Reading: Dixit and Nalebuff, “Thinking Strategically: The Competitive Edge in Business and Everyday Life”, Norton. Tests: There will one midterm worth 25% and one final worth 50%. The remaining 25% will be earned via participation in in-class games. Exam Schedule: Midterm Thursday October 3 1st Final Thursday December 12 th, 1.00pm. Office Hours: Tuesdays and Thursdays 3.30-4.30 and by appointment.
Games People Play. Games People Play The “Games of Strategy” strategy 1 st edition - $35 (approximately) 2 nd edition - $96.25 (from the Norton web site) Your best strategy – buy used!! Yes we can conclude Dixit and Skeath “wrote the book” on games
Games People Play. Games People Play Course Outline 1.Basic Ideas and Examples Dixit and Skeath Chapter 1 2.How to Think About Strategic Games Dixit and Skeath Chapter 2 3.Sequential Move Games Dixit and Skeath Chapter 3 4.Simultaneous Move Games with Pure Strategies Dixit and Skeath Chapters 4 and 5 5.Mixed Strategies Dixit and Skeath Chapters 7 and 8 6.Combining Simultaneous and Sequential Moves Dixit and Skeath Chapter 6 7.Uncertainty and Information Dixit and Skeath Chapter 9
Games People Play. Games People Play Course Outline (continued) 8.Strategic Moves Dixit and Skeath Chapter 10 9.The Prisoner’s Dilemma and Repeated Games Dixit and Skeath Chapter 11 10.Collective Action Games Dixit and Skeath Chapter 12 11.Evolutionary Games Dixit and Skeath Chapter 13 12.Brinksmanship: The Tragic Tale of George and Saddam Dixit and Skeath Chapter 14 13.Auctions Dixit and Skeath Chapter 16 14.Bargaining Dixit and Skeath Chapter 17
Games People Play. When you see and hear it’s time to play a game!!
Games People Play.
The Name Game Students should divide themselves into groups of 5-8 individuals Each group must select a crazy name The groups will then vote on which name is the craziest The group with the most votes wins
Games People Play. Real Minor League Baseball Team Names Boise Irrigators Union Cedertown Sea Cows Centralia ZerosCorsicana Gumbo Busters Des Moines UndertakersEau Claire Puffs Freeport PretzelsFresno Raisin Eaters High Point Furniture MakersHolyoke Paperweights Hoquiam Perfect Gentlemen Ilion Typewriters Iola GasbagsJackson Blind Tigers Kalamazoo Celery EatersKirksville Osteopaths Mayfield PantmakersMinot Why Nots Montpelier GoldfishMuncie Fruit Jars Nevada LunaticsWilkesboro Flashers Paris ParasitesRacine Malted Milks Regina BonepilersSpringfield Babes Troy WasherwomenUtica Pent-Ups Vancouver Horse DoctorsWaterloo Loons Waterloo MicrobesWaycross Blowhards Zanesville Flood Sufferers
Games People Play. 1: Basic Ideas and Examples Classification of Games Cooperative or non-cooperative Zero-sum or non-zero-sum Full information or incomplete information Sequential or simultaneous One-shot or repeated or recurring Fixed or manipulable rules Enforceable or unenforceable agreements
Games People Play. Classification of Games The point of coming up with a classification of games is to allow us to identify the precise nature of the situations we find ourselves in. This is an essential first step to determining what strategies we expect our opponents to follow, and what strategies are in our best interests. Also if we identify that we are playing a game in which we are at a disadvantage then we can attempt the change the game we are playing. Example: Example: A firm is engaged in bargaining over the price of an input. They find they have a very weak position. One possibility is not to bargain. Instead put a supply contract out for tenders!!
Games People Play. Classification of Games Cooperative or non-cooperative Are the players interests in conflict or not? In cooperative games the players interests are aligned. In non-cooperative games their interests are either partially or totally in conflict.
Games People Play. Classification of Games Zero-sum or non-zero-sum In a zero sum game one players gain is precisely the other players loss. A coin flip is a zero sum game. A non-zero-sum game has the property that whatever is to be divided between the players changes with the actions they take.
Games People Play. Classification of Games Full information or incomplete information In a full information game all players know everything about the game. In an incomplete information game the value to the other player of the outcomes of the game is imperfectly known.
Games People Play. Classification of Games Sequential or simultaneous In a sequential game the players take it in turns to move. Example: Chess is a sequential game. In a simultaneous game all players move at the same time. Example: Rock-Paper-Scissors.
Games People Play. Classification of Games One-shot or repeated or recurring Is the game played once? Repeatedly with the same opponent? Repeatedly but with different opponents?
Games People Play. Classification of Games Fixed or Manipulable Rules In a fixed rule game the rules are given Example: Chess In a manipulable rule game the rules are determined by pre-play Example: Setting a legislative agenda
Games People Play. Classification of Games Enforceable or unenforceable agreements Enforceable agreements can be determined and enforced via sanctions stipulated in the contract Example: A contractor often has to pay a penalty if a job is not completed on time Unenforceable agreements Example: The promise of aid from one sovereign nation to another
Games People Play. Terminology and Definitions PlayersStrategiesPayoffsRationality Common knowledge of rules Equilibrium Evolutionary games Experimental games
Games People Play. Terminology and Definitions Players. The players in a game are individuals, or groups of individuals acting collectively (e.g. firms, government departments, countries etc.)
Games People Play. Terminology and Definitions Strategies The choices available to the players. If the game is sequential then strategy refers to the players plans, and may involve rules like: If he plays A then I will play B, otherwise I will play C.
Games People Play. Terminology and Definitions Payoffs What the players receive as the result of the various possible outcomes of the game. These may be measured in dollars, happiness, prestige, or possibly grades.
Games People Play. Terminology and Definitions Rationality We assume that players follow their best strategies: those that realize the highest expected payoff.
Games People Play. Terminology and Definitions Common knowledge of rules We assume that the players have a common understanding of the rules of the game. This does not mean that we cannot allow for surprises or unforeseen circumstances. These are possibilities to which a very small probability is attached. Hence this assumption is not restrictive at all.
Games People Play. Terminology and Definitions Equilibrium This is the result of the game. When each player has made all their rational moves and neither wants to change, then we have found the solution. This is the definition of an equilibrium. The equilibrium of a game is what we expect and predict will happen.
Games People Play. Terminology and Definitions Evolutionary games Some games are not based on the concept of equilibrium. They are based on reactive learn-by- experience, and from observing others behavior. We then look for evolutionary stable states.
Games People Play. Terminology and Definitions Terminology and Definitions Experimental games Games played under experimental conditions. In the lab. We shall play many such games.
Games People Play.
The p-Beauty Contest Game Objective Choose a number between 0 and 100. If the number you choose is the closest to 2/3 of the average of all the other players choices, you win.
Games People Play. The p-Beauty Contest Game Background A beauty contest game because it bears strong resemblance to newspaper beauty contests discussed by John Maynard Keynes (famous English economist) 60 years ago A collection of women's faces printed in the newspaper The object: To pick those that would be rated "prettiest.“ The strategy: One should not vote for the faces he or she truly thought were prettiest or even the ones he or she thought most people would think were prettiest but the ones that one thought most people would think that most people would think were the prettiest, and so on
Games People Play. The p-Beauty Contest Game The equilibrium of this game is to choose zero!! Most people don’t choose zero Explanation #1: A person might not be so clever, and only reasons one or two levels deep into the iterated process.
Games People Play. The p-Beauty Contest Game Explanation #2 A person fully realizes 0 is the equilibrium of the game but does not believe that other players are equally clever. Because a player did not pick 0, we cannot infer that the player is irrational. It can only be inferred that rationality is not common knowledge. After all, a person who selected 0 would not win. Without common knowledge, any number selected below 75 can be justified. In other words, a rational person can pick a number greater than zero, but only if she believes some in the group to be irrational.
Games People Play. The p-Beauty Contest Game Winning strategy: To win the p-beauty contest, you have to be just one step smarter than the average person, but not too clever. If you are too clever, you will select a number too low. Think of a seller in the stock market. He wants to sell his shares just before the average person is selling, when the price of the share is at its peak. Therefore, he does not want to sell it too early.