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1 1 Deep Thought BA 592 Lesson I.1 Introducing Games I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they’d never expect it. --- by Jack Handey.

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2 2 Acknowledgements The course content is adapted from the textbook Games of Strategy third edition, published by W.W. Norton & Company © Welcome to BA 592 Game Theory BA 592 Lesson I.1 Introducing Games

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3 3 Getting acquainted What is Game Theory? Game Theory finds optimal decisions when payoffs to a player depend on the decisions of other players as well as the player himself. Game Theory is also known as multi-person decision theory. The course focuses on formulating and solving games to find optimal business strategies and economic policies. Applications include bargaining, lending, dividing pirate gold, …. BA 592 Lesson I.1 Introducing Games Welcome to BA 592 Game Theory

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4 4 Welcome to BA 445 Managerial Economics BA 592 Lesson I.1 Introducing Games Getting started Read and bookmark the online course syllabus. It serves as a contract specifying our obligations to each other. (You may need to use Internet Explorer.) In particular, note: Introduction to Microeconomics, Statistics, and Calculus are prerequisites, so review as needed. Before each class meeting, download and read the PowerPoint lesson, as presented under the “Schedule” link.

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5 5 Lesson overview BA 592 Lesson I.1 Introducing Games Chapter 1 Basic Ideas and Examples Lesson I.1 Introducing Games What is a Game? Example 1: Prisoners’ Dilemma Example 2: Penalty Kick Example 3: Predicting Current Strategies Example 4: Predicting Future Strategies

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6 6 What is a Game? There are many types of games --- board games (Monopoly, …), card games (poker, …), video games (Warcraft,…), and field games (football,…). We focus on games where: n There are 2 or more players. n There is some choice of action where strategy matters. n The game has outcomes; often, someone wins, someone loses. n Outcomes depend on the strategies chosen by all players: there is strategic interaction. What does that rule out? n Games of pure chance, like lotteries and slot machines, since strategies don't matter. n Games without strategic interaction between players, like Solitaire; there are strategies, but no interaction. BA 592 Lesson I.1 Introducing Games What is a Game?

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7 7 Why Study Games? Games aim to be useful models of strategic interactions among economic agents. Many business and economic decisions involve strategic interaction. n Behavior in imperfectly competitive markets, like Coca- Cola versus Pepsi. n Behavior in economic negotiations, like wages. n Behavior in auctions, like investment banks bidding on U.S. Treasury bills. Game theory is not limited to Business and Economics. n The Cuban Missile Crisis was a game of chicken. BA 592 Lesson I.1 Introducing Games What is a Game?

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8 8 Game Theory is useful for explanation. Economic historians ask: Why did that happen? Why did two agents hurt each other, rather that cooperate? n Why did makers of personal computers engage in cutthroat competition that resulted in bankruptcies? n Why did the U.S. and Soviet Union spend so much money on the arms race? Why did other agents cooperate, and avoid competition? n Why is the OPEC cartel sometimes effective at raising the price of oil? BA 592 Lesson I.1 Introducing Games What is a Game?

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9 9 Game Theory is useful for prediction. Economists ask: What will happen after a change in public policy?Economists ask: What will happen after a change in public policy? Will two agents continue to hurt each other?Will two agents continue to hurt each other? Will two agents continue to cooperate?Will two agents continue to cooperate? BA 592 Lesson I.1 Introducing Games What is a Game?

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10 Game Theory is useful for advice or prescription. Managers ask: Which strategies are optimal?Managers ask: Which strategies are optimal? Which are likely to lead to disaster?Which are likely to lead to disaster? BA 592 Lesson I.1 Introducing Games What is a Game?

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11 BA 592 Lesson I.1 Introducing Games Prisoners’ dilemma Example 1: Prisoners’ dilemma Prisoners’ dilemma 1.You are in a course graded on a curve: 20% A’s, …. 2.The other students agree to not work too hard. 3.You must decide whether to enter into that agreement. Can you trust other students to live up the agreement?Can you trust other students to live up the agreement? What factors would affect whether students can be trusted?What factors would affect whether students can be trusted? We begin studying repeated games in Part II of the course.We begin studying repeated games in Part II of the course. Can a prisoner trust his partner in crime to not confess?Can a prisoner trust his partner in crime to not confess? Can you trust your roommate with $10 left on a table? $1000?Can you trust your roommate with $10 left on a table? $1000? Can you trust a fellow Greyhound bus passenger with $1?Can you trust a fellow Greyhound bus passenger with $1?

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12 BA 592 Lesson I.1 Introducing Games Example 2: Penalty Kick Strategic Uncertainty is not knowing the strategies or actions of other players. You always want to reduce your own strategic uncertainty. Sometimes, you want to reduce the strategic uncertainty of your opponents, like telling them of your marketing a new drug so they will give up marketing a substitute drug. Other times, you want to increase your opponents’ strategic uncertainty.

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13 BA 592 Lesson I.1 Introducing Games Stopping a soccer penalty kick is quite a feat By Gary Mihoces, USA TODAY "When you consider that a ball can be struck anywhere from miles per hour, there's not a whole lot of time for the goalkeeper to react," says Bob Gustavson, professor of health science and men's soccer coach at John Brown University in Siloam Springs, Ark."When you consider that a ball can be struck anywhere from miles per hour, there's not a whole lot of time for the goalkeeper to react," says Bob Gustavson, professor of health science and men's soccer coach at John Brown University in Siloam Springs, Ark. Gustavson says skillful goalies use cues from the kicker. They look at where the kicker's plant foot is pointing and the posture during the kick. Some even study tapes of opponents. But most of all they take a guess — jump left or right after the kicker has committed himself.Gustavson says skillful goalies use cues from the kicker. They look at where the kicker's plant foot is pointing and the posture during the kick. Some even study tapes of opponents. But most of all they take a guess — jump left or right after the kicker has committed himself. Following an unpredictable strategy means randomly selecting one or more actions, like a goalie jumping left or jumping right.Following an unpredictable strategy means randomly selecting one or more actions, like a goalie jumping left or jumping right. The strategy can be right, even when the action fails!The strategy can be right, even when the action fails! We begin studying unpredictable strategies in Part II of the course.We begin studying unpredictable strategies in Part II of the course. Example 2: Penalty Kick

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14 BA 592 Lesson I.1 Introducing Games Example 3: Predicting Current Strategies Outcomes of a game depend on the strategies chosen by all players, so you should predict your opponents’ strategies before you choose your own. When your opponents’ strategies are chosen at the same time as yours, you must predict what your opponent will do now, recognizing that your opponent is doing the same.

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15 Guess 2/3 of the average 1.No talking or other communication between players. 2.Players secretly write a real number between 0 and The winner is the one closest to 2/3 of the average. 4.The winner in this class gets $1.00. If there is a tie, the $1.00 will be evenly divided. Why did you choose your particular number? Will you play differently next time? BA 592 Lesson I.1 Introducing Games Example 3: Predicting Current Strategies

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16 BA 592 Lesson I.1 Introducing Games Example 4: Predicting Future Strategies Opponents’ strategies might also be chosen after yours, so you must predict what your opponent will do in the future, recognizing that your opponent can react to your strategy.

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17 BA 592 Lesson I.1 Introducing Games Example 4: Predicting Future Strategies Five Pirates find 100 gold coins. They must decide how to distribute them. The Pirates have a strict order of seniority: Pirate A is senior to B, who is senior to C, who is senior to D, who is senior to E. The Pirate world's rules of distribution are thus: the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed distribution is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Pirates base their decisions on three factors. Firstly, each pirate wants to survive. Secondly, each pirate wants to maximize the amount of gold coins he receives. Thirdly, each pirate prefer to throw another overboard, if doing so does not decrease his own gold coins. Can Pirate A survive? If so, what distribution of coins should he propose?

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18 BA 592 Lesson I.1 Introducing Games Pirate A needs to predict which distributions are acceptable to the other pirates. That, in turn, depends on which distributions the other pirates can expect if they throw Pirate A overboard. To predict those distributions, start from the end of the possible ends of the game and work backward: If 2 pirates remain (D and E), D proposes 100 for himself and 0 for E. He has the casting vote, and so this is the allocation.If 2 pirates remain (D and E), D proposes 100 for himself and 0 for E. He has the casting vote, and so this is the allocation. If 3 pirates remain (C, D and E), C knows that D will offer E 0 in the next round; therefore, C has to offer E 1 coin in this round to make E vote with him and get his distribution through (he cannot offer less because E prefers to throw C overboard if he were offered 0 gold). Therefore, when only three pirates are left, the distribution is C:99, D:0, E:1.If 3 pirates remain (C, D and E), C knows that D will offer E 0 in the next round; therefore, C has to offer E 1 coin in this round to make E vote with him and get his distribution through (he cannot offer less because E prefers to throw C overboard if he were offered 0 gold). Therefore, when only three pirates are left, the distribution is C:99, D:0, E:1. Example 4: Predicting Future Strategies

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19 BA 592 Lesson I.1 Introducing Games If 4 pirates remain (B, C, D and E), B knows the distribution will be C:99, D:0, E:1 if he were thrown overboard. To avoid being thrown overboard, B can simply offer 1 to D (he cannot offer less because D prefers to throw B overboard if he were offered 0 gold). Because he has the casting vote, the support only by D is sufficient. Thus the distribution is B:99, C:0, D:1, E:0.If 4 pirates remain (B, C, D and E), B knows the distribution will be C:99, D:0, E:1 if he were thrown overboard. To avoid being thrown overboard, B can simply offer 1 to D (he cannot offer less because D prefers to throw B overboard if he were offered 0 gold). Because he has the casting vote, the support only by D is sufficient. Thus the distribution is B:99, C:0, D:1, E:0. When A proposes a distribution to all 5 pirates (A, B, C, D and E), A knows the distribution will be B:99, C:0, D:1, E:0 if he were thrown overboard. To avoid being thrown overboard, A can simply offer 1 to C and E (he cannot offer less because either C or E prefer to throw A overboard if he were offered 0 gold). Because he has the casting vote, the support only by C and E is sufficient. Thus A should propose A:98, B:0, C:1, D:0, E:1.When A proposes a distribution to all 5 pirates (A, B, C, D and E), A knows the distribution will be B:99, C:0, D:1, E:0 if he were thrown overboard. To avoid being thrown overboard, A can simply offer 1 to C and E (he cannot offer less because either C or E prefer to throw A overboard if he were offered 0 gold). Because he has the casting vote, the support only by C and E is sufficient. Thus A should propose A:98, B:0, C:1, D:0, E:1. Example 4: Predicting Future Strategies

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20 End of Lesson I.1 BA 592 Game Theory BA 592 Lesson I.1 Introducing Games

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