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Game Theory

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Poker Do you play poker? Do you play the probabilities? What happens when someone bluffs?

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John von Neumann 1928 - Mathematical genius von Neumann, 25, plays poker, invents game theory. Sees someone bluff and realizes that the best way to play the game is not to play the probabilities but to play according to what moves the competition makes. Figures out mathematically what the optimal moves are when two rational people play a game.

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Game theory is about not making moves in a vacuum, but about making moves based on your evaluation of what your opponents most likely moves will be. – And assuming that your opponent is rational and smart (able to think strategically). – Look forward and reason backward. Game theory is the science of rational behavior in interactive situations.

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1944 - von Neumann is a major force in inventing the atomic bomb and the modern computer. 1950 - Two Rand Corporation scientists invent the Prisoners Dilemma game.

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The Prisoners Dilemma In 1950 a conductor on a train to Kiev rehearses for a Tchaikovsky concert. KGB arrests him for subversive activity. KGB arrests Boris Tchaikovsky, a worker, on the streets of Kiev. KGB puts them in separate cells so they cant communicate. KGB offers them both a deal.

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The Prisoners Dilemma If the conductor turns state evidence against Boris (rats) and Boris doesnt, he gets one year in a gulag and Boris gets 25 years. If the conductor doesnt rat and Boris does, the conductor gets 25 years in a gulag and Boris gets only one year.

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The Prisoners Dilemma If both rat, each gets 10 years. If neither rats, each get three years (for doing nothing). The silent auction begins. – Because they cannot communicate, they must each figure out what they other will rationally do, and act accordingly. They are acting simultaneously.

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The Prisoners Dilemma Each serve 10 years, meet in the gulag, begin talking, and discover they ratted on each other. While talking they realize that if each had said nothing, they would only have been in for three years.

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Boris Conductor RatNot Rat Payoff Matrix Rat Not Rat 10, 10 *1, 25 25, 1 3, 3 * Conductor, Boris

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A Modern Game KAAA-TV, on the West Coast, is considering switching from its current prime time (8-11 p.m.) to early prime time (7-10 p.m.). KAAA is #2 in prime time, and because of KBBBs very strong 10-11 p.m. lead-in to its late news, KAAA is #2 in late news even though its news product is competitive. KBBB is #1 in late fringe also.

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KBBB-TV is #1 in prime time and has excellent 10-11 p.m. network lead-ins to its 11 oclock news, which puts it #1 in the late news race. KBBB is also #1 in late fringe. KCCC-TV is a weak #3 in prime time and late news. It is a network-owned station and will not switch to early prime. The solution of this problem requires looking forward and reasoning back.

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KAAA Decision Tree KAAA KAAA Go KBBB Go KBBB No Go KAAA No Go KBBB Go KBBB No Go

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Payoff Matrix KBBB KAAA Go No go GoNo Go 4, 2*3, 4 1, 3 2, 1 Assigning weights is the most difficult decision. * KAAA, KBBB

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KAAAs Payoff Weights 4,2 = If KAAA switches (go) to early prime and KBBB also switches (go), both gain more revenue from higher ratings for 10-10:30 p.m. late news. KBBB doesnt gain as much as it would if KAAA switches and KBBB doesnt (3,4).

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KAAAs Payoff Weights 3,4 = If KAAA switches (go) and KBBB doesnt switch (no go), KAAA gains revenue with its 10- 10:30 p.m. news, but the news is up against KBBBs strong prime and KBBBs late news gets higher ratings than before because KAAA has dropped news from the time period.

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KAAA Payoff Weights 1,3 = If KAAA doesnt switch (no go) and KBBB switches (go), KAAA loses big because its weaker 10-11 p.m. prime is up against strong KBBB news which has strong lead-ins and strong late fringe. 2,1 = If KAAA doesnt switch and KBBB doesnt switch, nothing happens, but the outcome isnt as bad as if KAAA doesnt switch and KBBB switches (1,3)

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KAAA Strategies Adding KAAA go weights (4+3 = 7) shows switching is the best strategy, because its no-go weights (1+2 = 3) are much worse. KBBBs assigned weights are the same with either decision (4+1 and 3+2 = 5).

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KAAA Strategies KAAAs best strategy is to falsely announce its staying with its current schedule, hoping KBBB will switch to gain an advantage and hurt KAAA (1,3). Then, at the last moment, KAAA switches to early prime to gain its maximum outcome (4,2), assuming KBBB stays with its decision to switch. Secrecy is an imperative.

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Strategic Moves Secrecy Commitment (burning the getaway boats) Threats and promises Deterrence and compellence Warnings and assurances Trial balloons False announcements Preemptive strikes Tit-for-tat Bluffs

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Strategies Tit-for-tit, while effective, leads to escalation in many situations. – The dollar auction A dollar bill is put up for sale; minimum bid one cent. Proceeds as a regular auction. One exception: Auctioneer must be paid by highest bidder, but also by the second highest bidder. – Winning bidders pay what they bid and receive a dollar. – Second-highest bidders pay what they bid and receive nothing. Game introduced in 1971. Thousands of games, average paid was $3.41

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Strategies Bluffing – Bluffers make statements, show behaviors, and perform activities that would be perfectly all right if they were not completely unfounded. – Bluffing is like vitamins. It is essential in small amounts, but harmful if used excessively. * Laszlo Mero, Moral Calculations, Copernicus, 1998.

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Mixed Strategy You cant bluff all the time, no one will believe you. If you never bluff, everyone will fold because they know youre telling the truth. You have to bluff occasionally. – A mixed strategy. – On a random basis: No identifiable pattern.

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Strategies Strategies depend on the game. – Sequential or Simultaneous Soccer goalie (sequential) Chicken (simultaneous) Gift of the Magi (simultaneous)

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Games Zero-sum games – Assume a winner (+1), and a loser (-1) Multi-player games – Marathon - 1000 racers, different niches (men-women), several winners – Business – a marathon – Business strategies are about getting more than your fair share (not necessarily winning as in a zero-sum game). Profit Market share Dominate a niche

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The Prisoners Dilemma If the prisoners had been able to communicate, what would have happened? If they had been given a chance to play the game again and again, what would have happened?

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The Prisoners Dilemma The rules for the game changes when you play repeatedly, as the Rand Corporation scientists discovered. And if the other side gets greedy (which is inevitable), you must use tit-for-tat. You must teach the other side cooperation (to accept three years in the gulag) – do whats best for both. Use game theory to force legal cooperation.

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Co-opetition * Customers Complementors Suppliers Competitors Business Ecosystem * Adam Brandenburger and Barry Nalebuff, Co-opetition, Currency Doubleday, 1996

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Co-opetition If you are Steve Jobs at Apple … What is Google? What is Intel? What is Microsoft? Remember, ecosystems co-evolve. – Wolves and caribou

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Co-opetition It might be a smart strategic move to change the game and the players. In fact, it might be a smart strategic move to pay someone to compete. – GE tried to get Time Warner to bid for NBC U

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Business Insanity Doing the same thing over and over and expecting different results. Brainstorm to find new and different solutions, think strategically, and use game theory. – Look forward and reason backward.

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Game Theory 1.

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