UC Berkeley: Game Theory, Slides of Game Theory

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UC Berkeley

Haas School of Business

Game Theory

(EMBA 296 & EWMBA 211)

Summer 2016

Preliminaries

Block 1

May 19-20, 2016

Game theory

Game theory is about what happens when decision makers (spouses, work-ers, managers, presidents) interact.

In the past

fi

fty years, game theory has gradually became a standard lan-

guage in economics.

The power of game theory is its generality and (mathematical) precision.

The

paternity

of

game

theory

As Milton Friedman said famously observed “theories do not have to berealistic to be useful.” A theory can be

useful

in three ways:

descriptive (how people actually choose)

prescriptive (as a practical aid to choice)

normative (how people ought to choose)

Aumann (1987):

Game theory is a sort of umbrella or ‘uni

fi

ed

fi

eld’ theory for the

rational side of social science, where ‘social’ is interpreted broadly,to include human as well as non-human players (computers, animals,plants).

Four examples

Example I: Hotelling’s electoral competition game

There are two candidates and a continuum of voters, each with a fa-vorite position on the interval

[

1]

Each voter’s distaste for any position is given by the distance betweenthe position and her favorite position.

A candidate attracts the votes o

ff

all citizens whose favorite positions

are closer to her position.

Hotelling with two candidates class experiment

• 1 .9 .8 .7 .6 .5 .4 .3 .2 .1 -. Fraction -. -. -. -. -. -. -. -. -. -. -. -.

Example II: Keynes’s beauty contest game

Simultaneously, everyone choose a number (integer) in the interval [

100]

The person whose number is closest to

of the average number

wins a

fi

xed prize.

John Maynard Keynes (1936):

It is not a case of choosing those [faces] that, to the best of one’s

judgment, are really the prettiest, nor even those that average opin-ion genuinely thinks the prettiest.

We have reached the third degree

where we devote our intelligences to anticipating what average opinionexpects the average opinion to be. And there are some, I believe, whopractice the fourth,

fi

fth and higher degrees.

self-ful

fi

lling price bubbles!

0

1-

6-

11-

15

16-^20

21-

25

26-^30

31-

35

36-^40

41-

45

46-

50

51-

55

56-^60

61-

65

66-^70

71-

80

81-

90

91- 100

0.15 0.

Students

Managers

PhDs

CEOs

Trustees

Example

III:

the

centipede

game

(graphically

resembles

a

centipede

insect)

D

D

D

D

D

D

C

C

C

C

C

C

1

1

1

2

2

2

100

0

0

200

300100

200400

500300

400600

600500

Example IV: auctions From Babylonia to eBay, auctioning has a very long history.

Babylon:

• women at marriageable age. Athens, Rome, and medieval Europe: - rights to collect taxes, dispose of con

fi

scated property, lease of land

and mines,

and many more...

The word “auction” comes from the Latin

augere

, meaning “to increase.”

The earliest use of the English word “auction” given by the

Oxford English

Dictionary

dates from 1595 and concerns an auction “when will be sold

Slaves, household goods, etc.”In this era, the auctioneer lit a short candle and bids were valid only ifmade before the

fl

ame went out — Samuel Pepys (1633-1703) —