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Game Theory

Game Theory. “ In War the Will Is Directed at an Animate Object That Reacts .” - Karl Von Clausewitz, On War Mike Shor Lecture 2. Review. Game Theory Description of strategic interaction between mutually aware players You are self-interested and selfish So is everyone else Tools

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Game Theory

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  1. Game Theory “In War the Will Is Directed at an Animate Object That Reacts.” - Karl Von Clausewitz, On War Mike Shor Lecture 2

  2. Review • Game Theory • Description of strategic interaction between mutually aware players • You are self-interested and selfish • So is everyone else • Tools • Recognize you are in a game • Recognize the type of game • Know the possible outcomes • Manipulate the game structure Game Theory - Mike Shor

  3. Rules of the Game • The strategic environment • Players • Strategies • Payoffs • The rules • Timing of moves • Nature of conflict and interaction • Informational conditions • Enforceability of agreements or contracts • The assumptions • Rationality • Common knowledge Game Theory - Mike Shor

  4. The Strategic Environment • Players • Everyone who has an effect on your earnings • Strategies • Complete plan of action • Specifies a decision for each possible decision • Tactics vs. Strategies vs. Moves • Payoffs • Numbers associated with each possible outcome • Expected payoffs if outcomes are random Game Theory - Mike Shor

  5. The Rules • Timing of moves • Are the moves simultaneous? Sequential? • Nature of conflict and interaction • Are players’ interests in conflict? Cooperation? • Will players interact once, or repeatedly? • Informational conditions • Is there full information? Advantages? • Enforceability of agreements or contracts • Can agreements to cooperate work? Game Theory - Mike Shor

  6. Example: Toys “R” Us • Players • Toys R Us • Warehouse clubs: Costco, Pace • Manufacturers: Hasbro, Mattel, etc. • Strategies • To threaten or not to threaten • To deal or not to deal with warehouse clubs • To follow through on threats or not Game Theory - Mike Shor

  7. Rules • Sequential timing • Threat  Manufacturer’s decisions • How will my opponents react? • Simultaneous timing • Manufacturer’s decisions • What is my opponent doing right now? • Information • Future profitability of warehouse clubs • What can I infer from the actions of others? • Agreements • Enforceability of contracts & agreements • What happens if someone cheats? Game Theory - Mike Shor

  8. Changing the Rules • Are the rules of the game fixed? • Example: voting and agenda setting COMMANDMENT When the rules of the game are flexible manipulate them to your advantage. Game Theory - Mike Shor

  9. Before the Supreme Court:Gore v. Bush • Four judges prefer: Bush to Gore to Remand (B>G>R) • Three judges prefer: Gore to Remand to Bush (G>R>B) • Two judges prefer: Remand to Bush to Gore (R>B>G) No majority in three-way race Chief justice selects voting order: • B v. G than winner v. R • B v. R than winner v. G • G v. R than winner v. B Game Theory - Mike Shor

  10. Member Preferences • Preferences: • 4: B > G > R • 3: G > R > B • 2: R > B > G • Majority rule results: • B beats G ; G beats R ; R beats B Game Theory - Mike Shor

  11. Rules of Voting • Majority rule results: • B beats G ; G beats R ; R beats B • B vs. G then winner vs. R  R • B vs. R then winner vs. G  G • G vs. R then winner vs. B  B Game Theory - Mike Shor

  12. The Assumptions • Rationality • Players aim to maximize their payoffs • Players are perfect calculators • Common knowledge • Each player knows the rules of the game • Each player knows that each player knows the rules • Each player knows that each player knows that each player knows the rules • Each player knows that each player knows that each player knows that each player knows the rules • Each player knows that each player knows that each player knows that each player knows that each player knows the rules • Etc. etc. etc. Game Theory - Mike Shor

  13. Examples • Biased beauty contest • (3/4)  100 = 75 • (3/4)  75  56 • (3/4)  56  32 • 24, 18, 14, 10, 8, 6, 4, 3, 2, 1, 0 • Intentional failure to coordinate • Bluffing Game Theory - Mike Shor

  14. The Stock Market& Rationality • “He who panics first wins.” i.e. Sell before everybody else does. • When would the sell-off occur if we knew the exact date of the bubble’s burst? Game Theory - Mike Shor

  15. “Now keep in mind this is just a ballpark figure”

  16. Equilibrium • What is likely to happen when rational players interact in a game? • Type of equilibrium depends on the game • Simultaneous or sequential • Perfect or limited information • Concept always the same: • Each player is playing the best response to other players’ actions • No unilateral motive to change • Self-enforcing Game Theory - Mike Shor

  17. Summary • Recognizing that you are in a game • Identifying players, strategies, payoffs • Understanding the rules • Manipulating the rules • Next time: Equilibrium • Searching for possible outcomes Game Theory - Mike Shor

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