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Game Theory 1

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**Poker Who plays? Do you play the probabilities?**

Reading other hands is the most important element in playing winning poker. Playing the probabilities in judging hands seems like a rational strategy. Playing rationally by using probability theory assumes that it is the only factor in winning--betting according to the power of your hand and your reading of other hands. It assumes that the other players will make rational decisions. But what if somebody bluffs--you never know afterwards how to predict his or her hand. That’s when use game theory--the notion that you play according to your mathematical assessment of what other players’ strategies are and what your risk-reward ratio is according to their strategies. 2

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**John von Neumann “The best mind of the 20th Century”**

Mathematical genius von Neumann, 25, plays poker, invents game theory. The odds are meaningless when someone bluffs. Von Neumann is a major force in inventing the atomic bomb and the modern computer. Two Rand Corporation scientists invent the Prisoner’s Dilemma game. von Neumann born in Budapest. Jewish. Father a banker. Photographic memory--extremely rare. Played phone-book game with family’s friends when young. Published first paper on mathematics when he was 18. Got Ph.D. in mathematics with a minor in physics and chemistry in just 5 years of college. Met Robert Oppenheimer in German in In 1929 went to Princeton as Assistant Professor. In 1933 went to the Institute for Advanced Study at Princeton when it opened. Was the youngest professor there. Had an office a few doors from Einstein’s. Spoke seven languages fluently and could also translate into Greek and Latin. Worked on the atomic bomb in the Manhattan Project. Did calculations in his head. Instrumental in developing modern computer, is credited with inventing punch cards for IBM. Consulted with IBM. Invented storing numbers digitally (0s and 1s). Wrote machine code in his head. “IBM’s owes half of its profits to von Neumann” - Edward Teller. When Princeton’s first computer was built, they gave it a complex math problem to solve. But to see if it was right, they gave the same problem to von Neumann, who figured it out in his head before the computer got it. 3

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Game Theory You have to take into consideration the objectives and strategies of the other players. Not just the probabilities Not just your own goals and strategies Your moves depend on their moves.

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**The Prisoner’s 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 can’t communicate. KGB offers them both a deal. 4

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**The Prisoner’s Dilemma**

If the conductor rats and Boris doesn’t, he gets one year in a gulag and Boris gets 25 years. If the conductor doesn’t rat and Boris does, he gets 25 years in a gulag and Boris gets one year. 5

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**The Prisoner’s Dilemma**

If both rat, each gets 10 years. If neither rats, each get three years. The silent auction begins.

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**The Prisoner’s Dilemma**

Each serving 10 years, they 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. 6

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

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

25, 1 Not Rat * Conductor, Boris 7

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Scenario 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 KBBB’s very strong 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. 8

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Scenario KBBB-TV is #1 in prime time and has excellent p.m. network lead-ins to its 11 o’clock 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. 9

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

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**Payoff Matrix Assigning weights is the most difficult decision. KBBB**

Go No Go Go 4, 2* 3, 4 * KAAA, KBBB KAAA 2, 1 1, 3 No go Assigning weights is the most difficult decision. 11

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KAAA’s 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 doesn’t gain as much as it would if KAAA switches and KBBB doesn’t (3,4). 12

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KAAA’s Payoff Weights 3,4 = If KAAA switches (go) and KBBB doesn’t switch (no go) , KAAA gains revenue with its 10-10:30 p.m. news, but the news is up against KBBB’s strong prime and KBBB’s late news gets higher ratings than before because KAAA has dropped news from the time period. 13

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KAAA Strategies 1,3 = If KAAA doesn’t switch (no go) and KBBB switches (go), KAAA loses big because its weaker p.m. prime is up against strong KBBB news which has strong lead-ins and strong late fringe. 2,1 = If KAAA doesn’t switch and KBBB doesn’t switch, nothing happens, but the outcome isn’t as bad as if KAAA doesn’t switch and KBBB switches (1,3) 14

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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. KBBB’s judged weights are the same with either decision (4+1 and 3+2 = 5). 15

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KAAA Strategies KAAA’s best strategy is to announce it’s 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 critical. 16

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Game Theory See “Game Theory- Sales ” case on

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**Anyone want to buy a $20 bill?**

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**The Prisoner’s 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 Prisoner’s 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)--to do what’s best for both. 17

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**Co-opetition Customers Competitors Complementors Suppliers**

Business Ecosystem 18

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**Co-opetition What are syndicators? What are other TV stations?**

Strategy: “Help Your Competitors Get Rich” Remember, Ecosystems Co-evolve. Wolves and caribou 19

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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 (co-opetition). Coke, Pepsi and NutraSweet Lin, McCaw and Bell South 20

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**The lessons are: Know what game you’re playing**

Know the rules of the game Play to win-win (cooperate)

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Nash’s Theorem Theorem (Nash, 1951): Every finite game (finite number of players, finite number of pure strategies) has at least one mixed-strategy Nash.

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