Download Economics 414 Game Theory Outline About Me: Peter Cramton

Economics 414
Game Theory
Outline
aIntroduction
aSyllabus
aWeb demonstration
aExamples
Professor Peter Cramton
Spring 2005
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About Me: Peter Cramton
Course Objectives
a B.S. Engineering, Cornell University
a Ph.D. Business & Economics, Stanford University
a Associate Professor, Yale University, 1984-93
a National Fellow, Hoover Institution, Stanford
University, 1992-93
a Professor of Economics, University of Maryland, since
1993
a Chairman, Market Design Inc., since 1995
a Chairman, Spectrum Exchange, since 1999
a President, Criterion Auctions, since 2000
aTo understand the importance of
competitive and cooperative factors in a
variety of decision problems
aTo learn how to structure and analyze
these problems from a quantitative
perspective
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Course Outline
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Logistics
aMeet Tuesday and Thursday, 9:30 – 10:45
aProblem Sets (about 6) and Web Exercises
[20% of grade]
aStrategic-Form Games
aExtensive-Form Games
aRepeated Games
aBayesian Games and Bayesian Equilibrium
aDynamic Games of Incomplete Information
aBargaining Theory
aAuction Theory (and Practice)
`Must be own work; don’t look at past solutions
`Small discussion groups fine
aMidterm Exam [30% of grade]
aFinal Exam [50% of grad]
`Tuesday, May 17, 8-10 am
aOffice Hours Tues 7:30 to 9:30 am
`Tydings 4101a
`301.405.6987 or [email protected]
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Did you get my email?
Web exercises
aEmail sent to
[email protected]
aIf you did not get it, then either:
aRegister at http://gametheory.tau.ac.il/
(student’s registration in upper right)
aYour login name will be:
`University has wrong email address for you
`You are not registered for this class (e.g. you
are on the waitlist)
`Your mail quota is exceeded
`CR479U<student e-mail>
where <student e-mail> is your full email.
aThe class password is:
`e139288Zt
aI will send an email with assignments
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Readings
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Introduction and Examples
aMartin J. Osborne, An Introduction to
Game Theory, Oxford University Press
(2004) [Required]
aWeb site: www.cramton.umd.edu
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Definition
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Game 1
Game theory is the study of mathematical
aEach of three players simultaneously picks
a number from [0,1]
aA dollar goes to the player whose number
is closest to the average of the three
numbers
aIn case of ties, the dollar is split equally
models of conflict and cooperation
between intelligent and rational decision
makers.
aRational: each individual maximizes her
expected utility
aIntelligent: individual understands
situation, including fact that others are
intelligent rational decision makers
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Game 1 in Normal Form
(Strategic Form)
Game 2: Both Pay Auction
aplayer i ∈ N = {1,...,n}
astrategy si ∈ Si
astrategy vector (profile)
s = (s1,...,sn) ∈ S = S1×...×Sn
apayoff function ui(s):S→ℜ, which maps
strategies into real numbers
agame in normal form Γ =
{S1,...,Sn;u1,...,un}
a$10 is auctioned to highest of two bidders
aPlayers alternate bidding
aAt each stage, bidding player must decide
either to raise bid by $1 or to quit
aGame ends when one of the two bidders
quits in which case the other bidder gets
the $10, and both bidders pay the
auctioneer their bids
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Game 2 in Extensive Form
(Game Tree)
Game in Extensive Form
aWho plays when?
aWhat can they do?
aWhat do they know?
aWhat are the payoffs?
$1
R
$2
R
2
Q
1
Q
Q
Q
Q
1
2
$3
R
1
$4
R
$5
R
1
...
-3, 6
7, -2
-1, 8
9, 0
0, 10
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Game 4
Game 3
1
l
1: 0
2: 2
1
L
R
2
2
r
l
3
1
-1
-1
L
R
2
r
l
2
0
1: 0
2: 2
17
r
l
3
1
-1
-1
r
2
0
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Game 3: How many info
sets?
Definitions
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aStrategy: a complete plan of action
(what to do in every contingency)
aInformation Set: for player i is a
collection of decision nodes satisfying
two conditions: player i has the move at
every node in the collection, and i
doesn't know which node in the
collection has been reached
l
1: 0
2: 2
L
R
2
2
r
l
3
1
-1
-1
r
2
0
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Game 4: How many info
sets?
More Definitions
1
L
a Perfect Information: each information set is
a single node (Chess, checkers, go, ...)
aFinite games of perfect information can be
"solved" by backward induction in the
extensive form or elimination of weakly
dominated strategies in the normal form
a Imperfect Information: at some point in the
tree some player is not sure of the complete
history of the game so far
R
2
l
1: 0
2: 2
r
l
3
1
-1
-1
r
2
0
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Game 3: Backward Induction
Looking ahead and reasoning back
1
l
1: 0
2: 2
L
R
2
2
r
l
3
1
-1
-1
20
r
2
0
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