game theory presentation 1229367921111224 2

7/21/2019 Game Theory Presentation 1229367921111224 2

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Abbas Keramati ( Assistant Professor)

University of Tehran MBAFall 2008

Game Theory Quantitative Analysis for Decision Making

M.hotbi

M.Pa!ho"h #iya


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Title

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Outline

What is Game Theory? History of Game Theory

Applications of Game Theory

Key Elements of a game Types of games

Nash Equilibrium (NE

!ure "trategies # $i%e& "trategie

'players ero)"um games


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hat is Game Theory?

*n strategic games+ agents choose

strategies that ,ill ma%imi-e theirreturn+ gi.en the strategies theother agents choose/

The mathematics of humaninteractions


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History of Game Theory

.on Neumannwrote a key paper in1928

1944 !Theory of Games and Economic

Behavior"y von #eumann and$orgenstern

19%& Nashinvents concept o' #as(e)uili"rium

*ame t(eory "ooms a'ter t(is+

1994 Harsanyi,Nash, and "eltenwin #o"el ri-e in economics 'or game

t(eory work


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$at(ematics

omputer /cience

0iology

conomics

olitical /cience

nternational

3elations

(ilosop(y

syc(ology

Law

$ilitary /trategy

$anagement

/ports

*ame laying

Applications of GameTheory


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Key Elements of a game

!layers (o is interacting5

"trategies (at are t(eir optio

!ayo0s (at are t(eir incentive

*nformation (at do t(ey know 1ationality 6ow do t(ey t(ink5


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Types of games

2ooperati.e or non)cooperati.e

ero sum an& non)-ero sum

"imultaneous an& sequential

!erfect information an& imperfect

information

3inite # *n4nite "trategies


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0

:1 :2 $inimum

;1 1& < =12

$a%imum 1& >5

6

An E%ample7


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Nash Equilibrium (NE

A players best strategy isA players best strategy is

that strategy that maximizesthat strategy that maximizes

that players payoff (utility),that players payoff (utility),

knowing the strategy's of theknowing the strategy's of the

other players.other players.


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')players ero)"umgames

-1 , 1 1 , -1

1 , -1 -1 , 1Player

Player !

enny $atc(ing ac( o' t(e two players (as a penny.

Two players must simultaneously c(oose w(et(er

to s(ow t(e 6ead or t(e Tail.

0ot( players know t(e 'ollowing rules =' two pennies matc( ?"ot( (eads or "ot(

tails@ t(en player 2 wins player 1As penny.

=Bt(erwise, player 1 wins player 2As penny.

"ail

#ea$

"ail

#ea$


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!risoner8s 9ilemma

#o communication

= /trategies must "e undertaken wit(out

t(e 'ull knowledge o' w(at t(e ot(erplayers ?prisoners@ will do.

layers ?prisoners@ develop dominant strategies

"ut are not necessarily t(e "est one.


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Ted

on'ess #ot on'ess

on'ess

0ill

#ot on'ess

0ot( get %years

1 year 'or0ill

1& years 'orTed

1& years 'or0ill

1 year 'orTed

0ot( get C

years

ayoD $atri 'orrisonerAs Eilemma


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An E%ample of

$i%e& "trategy game

0

0"elieves

0

doesnAt"elieve

"luDs 1 &

doesnAt"luD

& &.%


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No, let8s !lay This Game

Pirate Game

A

B

D

C

E


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Nash8s Equilibrium

T(is e)uili"rium occurs w(en eac( playerAsstrategy is optimal, knowing t(e strategys o' t(eot(er players.

playerAs "est strategy is t(at strategy t(atmaimi-es t(at playerAs payoD ?utility@, knowingt(e strategys o' t(e ot(er players.

/o w(en eac( player wit(in a game 'ollows t(eir

"est strategy, a #as( e)uili"rium will occur.


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9e4nition7 NashEquilibrium

Given others

choices, layer icannot !e !etter"off

if she #eviates from

si$


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Nashs Equilibrium cont.:

Bayesian Nash Equilibrium

T(e #as( )uili"rium o' t(e imper'ect=in'ormation game

% 0ayesian )uili"rium is a set o' strategies suc(t(at eac( player is playing a "est response, givena particular set o' "elie's a"out t(e move "ynature.

% ll players (ave t(e same prior "elie's a"out t(epro"a"ility distri"ution on natureAs moves.

% /o 'or eample, all players t(ink t(e odds o' player 1"eing o' a particular type isp, and t(e pro"a"ility o' (er"eing t(e ot(er type is 1-p


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Eiit and #ale"uD ThinkingStrategically

Eutta

Strategies and Games: Theoryand Practice

www.gamet(eory.net

$efrences
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game theory presentation 1229367921111224 2

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