Game Theory and its application.pptx

8/14/2019 Game Theory and its application.pptx

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*Strategic decisions making by intelligent rational thinkers

*Helps decision making under uncertainty

*Taking your best decision considering the rivals best move

Not Applicable to

*Games of pure chance, e.g. lotteries, slot machines. (Strategiesdon't matter).

*Games without strategic interaction between players


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*Two Prisoners, Ramesh & Suresh

*Each prisoner has two possible actions.

* Ramesh: Don't Confess, Confess

* Suresh: Don't Confess, Confess

*Prisoners choose actions simultaneously without knowing theaction chosen by the other.

*Consequences quantified in prison years.

* If neither confesses, each gets 1 year

* If both confess, each gets 5 years

* If 1 confesses, he goes free and other gets 15 years

*Fewer years=greater satisfaction=>higher payoff.


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We have your friend Ramesh and he is starting

to talk

Will Suresh confess?

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Confess Dont ConfessSuresh

Ramesh

Confess

Dont Confess

( -5, -5)

( -15, 0)

( 0, -15)

( -1, -1)

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Nash to help out Ramesh


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Nash Equilibrium

Neither player has an incentive to change strategy, given

the other players choice

If Suresh commits to Dont Confess, Ramesh has anincentive to confess

If Ramesh commits to Dont Confess, Suresh has anincentive to confess


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Conclusion:

The Suresh will confess

And Ramesh?

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Conclusion:

Ramesh confesses also

Best Decisions of both strategic players

Dont even get the 2ndbest

Both get 5 years, even though if they cooperated,they could get off with one year each

For both, confession is a dominant strategy: astrategy that yields a better outcome regardlessof the opponents choice

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What would the Ramesh and Suresh decide if they

could negotiate?

They could both become better off if they reachedthe cooperative solution.

which is why police interrogate suspects in separate rooms.

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Tit for Tat

Tit for Two Tat

Suspicious Tit for Tat

Free Rider

Always Cooperate

Axelrods Tournament


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Tit for Tat

Tit for Two Tat

Suspicious Tit for Tat

Free Rider

Always Cooperate

Axelrods Tournament


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*The action chosen is based on the opponents last

move.

*On the first turn, the previous move cannot be known,so always cooperate on the first move.

* Thereafter, always choose the opponents last move as

your next move.

*Nice; it cooperates on the first move.

* Regulatory; it punishes defection with defection.

* Forgiving; it continues cooperation after cooperation

by the opponent.

* Clear; it is easy for opponent to guess the next move,

so mutual benefit is easier to attain.


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*Same as Tit for Tat, but requires two consecutivedefections for a defection to be returned.

* Cooperate on the first two moves.

* If the opponent defects twice in a row, choose defectionas the next move.

*Key Points of Tit for Two Tat

*When defection is the opponents first move, this strategyoutperforms Tit for Tat

* Cooperating after the first defection causes the opponentto cooperate also. Thus, in the long run, both playersbenefit more points.


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*Always defect on the first move.

*Thereafter, replicate opponents last move.

*Key Points of Suspicious Tit for Tat

* If the opponents first move is defection, thisstrategy outperforms Tit for Tat

*However, it is generally worse than Tit for Tat.* The first move is inconsequential compared to

getting stuck in an infinite defection loop.


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*Always choose to defect no matter what the

opponents last turn was.

*This is a dominant strategy against an

opponent that has a tendency to cooperate.


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*Always choose to cooperate no matter what

the opponents last turn was.

*This strategy can be terribly abused by the

Free Rider Strategy.

*Or even a strategy that tends towards defection.


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*Took place in the early 1980s

*Professional game theorists were invited by Axelrodto submit their own programs for playing the

iterative Prisoners Dilemma.*Each strategy played every other, a clone of itself,and a strategy that cooperated and defected atrandom hundreds of times

*Tit for Tat won the first Tournament.*Moreover, Tit for Tat won a second tournament whereall 63 entries had been given the results of the firsttournament.

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Game Theory and its application.pptx