View
219
Download
0
Category
Preview:
Citation preview
8/14/2019 Game Theory and its application.pptx
1/19
*
8/14/2019 Game Theory and its application.pptx
2/19
*
*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
8/14/2019 Game Theory and its application.pptx
3/19
*
*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.
8/14/2019 Game Theory and its application.pptx
4/19
*
8/14/2019 Game Theory and its application.pptx
5/19
We have your friend Ramesh and he is starting
to talk
Will Suresh confess?
*
8/14/2019 Game Theory and its application.pptx
6/19
*
Confess Dont ConfessSuresh
Ramesh
Confess
Dont Confess
( -5, -5)
( -15, 0)
( 0, -15)
( -1, -1)
*
Nash to help out Ramesh
8/14/2019 Game Theory and its application.pptx
7/19
*
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
8/14/2019 Game Theory and its application.pptx
8/19
Conclusion:
The Suresh will confess
And Ramesh?
*
8/14/2019 Game Theory and its application.pptx
9/19
8/14/2019 Game Theory and its application.pptx
10/19
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
*
8/14/2019 Game Theory and its application.pptx
11/19
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.
*
8/14/2019 Game Theory and its application.pptx
12/19
*
Tit for Tat
Tit for Two Tat
Suspicious Tit for Tat
Free Rider
Always Cooperate
Axelrods Tournament
8/14/2019 Game Theory and its application.pptx
13/19
*
Tit for Tat
Tit for Two Tat
Suspicious Tit for Tat
Free Rider
Always Cooperate
Axelrods Tournament
8/14/2019 Game Theory and its application.pptx
14/19
*
*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.
8/14/2019 Game Theory and its application.pptx
15/19
*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.
8/14/2019 Game Theory and its application.pptx
16/19
*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.
8/14/2019 Game Theory and its application.pptx
17/19
*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.
8/14/2019 Game Theory and its application.pptx
18/19
*
*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.
8/14/2019 Game Theory and its application.pptx
19/19
*
*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.
Recommended