game theory ii: non-zero- sum gamesl3d.cs.colorado.edu/~ctg/classes/ai07/lectures/ai2007l26.pdf ·...
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Assignments
• Problem Set 4 due Thursday Dec. 6• Problem Set 5 due Thursday Dec. 13• Final exam Saturday Dec. 15• Review session evening of Thursday 12/13
(place and time TBA)
Evolutionary Game Theory
• Each animal can play one of two strategies:“hawk” and “dove”. Hawks always fightover a resource; doves retreat.
• When two hawks meet, they fight (assume a50 percent chance of winning).
• When two doves meet, they “display” andchoose the “winner” at random.
Looking for an “ESS”
• Here, neither “pure hawk” nor “pure dove” is anevolutionarily stable strategy (or ESS), since each can besuccessfully invaded by the other.
• Suppose our population isn’t all one or the other, butinstead has (in percentage) P hawks and (1-P) doves. Thepayoff to a newborn hawk is -25P + 50(1-P). The payoff toa new dove is 0P + (1-P)15. When these are equal, neitherstrategy is favored. So conceivably our population couldstabilize at a percentage P = 35/60 of hawks.
Games “in the Large”
• Games where I wish to do “X” only if fewpeople are doing “X”
• Games where I wish to do “X”only if lots ofpeople are doing “X”
• Public participation and anonymity• Behavioral game theory• I don’t want to play!
A Class-wide game
• If you choose “C”, you get N * 100 dollars.• If you choose “D”, you get 200 + (N * 100)
dollars.• N is the number of people who choose “C”.
I Don’t Want to Play!
• The “tragedy of the commons”• Game theoretic analysis of emotions• Ceding control:opting out of the game
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Qts/CowTotalQuarts
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Common sense says that victory goes to the side with themost intelligence, self-interest, coolness, options, power, andclear lines of communication. Common sense is wrong. Eachof these assets can be a liability in contests of strategy (asopposed to contests of chance, skill, or strength), wherebehavior is calculated by predicting what the other guy willdo in response....How do you persuade someone that you will not pay morethan $16,000 for a car that is really worth $20,000 to you?You make a public, enforceable $5,000 bet with a third partythat you won’t pay more than $16,000. As long as $16,000gives the dealer a profit, he has no choice but to accept....
Because an expensive threat works both ways, it can lead to acycle of self-incapacitation. Protesters attempt to block theconstruction of a nuclear power plant by lying down on therailroad tracks leading to the site. The engineer, beingreasonable, has no choice but to stop the train. The railroadcompany counters by telling the engineer to set the throttle sothat the train moves very slowly and then to jump out of thetrain and walk beside it. The protesters must scramble. Nexttime the protesters handcuff themselves to the tracks; theengineer does not dare leave the train. But the protesters mustbe certain the engineer sees them in enough time to stop. Thecompany assigns the next train to a nearsighted engineer.
- Pinker, How the Mind Works
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