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Mediators
Slides by Sherwin Doroudi
Adapted from “Mediators in
Position Auctions” by Itai Ashlagi,
Dov Monderer, and Moshe
Tennenholtz
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View Full Document Bayesian & PreBayesian
Games
•
Consider a game where every player has
private information regarding his/her “type”
•
A player’s
strategy
maps types to actions
•
Ex: You are either type A or type B and
you have actions “play” and “pass”; one
strategy might be A→ “play” and B→
“pass”; we can write this as (A, B) →
(“play”, “pass”)
Bayesian & PreBayesian
Games
•
These are games of
incomplete
information
•
In a
Bayesian Game
there is a commonly
known prior probability measure on the
profile of types
•
Ex: You are either type A or B, I am either
type X or Y, and we know that it is
common knowledge that our types are
equality likely to be (A, X), (A, Y), (B, X),
or (B, Y)
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View Full Document Bayesian & PreBayesian
Games
•
In a
preBayesian
game, there is no prior
probability over they types the players can
take
•
Ex: An auction setting in which there is no
known distribution with which the players
value the goods
•
We will be concerned only with pre
Bayesian games
Equilibria in PreBayesian
Games
•
When priors regarding types are not
known (i.e. in preBayesian game) we are
primarily concerned with
ex post
equilibrium
•
“A profile of strategies, one for each
player, such that no player has a profitable
deviation independently of the types of the
other players”
•
Requiring dominant strategies is stricter
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View Full Document Ex: PreBayesian Game
•
Game
H
: Assume player I has only one
type but player II is either type A or type B
5
2
3
0
0
0
4
2
I
II
α
β
α
β
Type(II) = A
2
2
0
0
3
3
5
2
I
II
α
β
α
β
Type(II) = B
Ex: PreBayesian Game
•
Game
H
: The ex post equilibrium is I plays
β and II plays (A, B) →(β, α)
5
2
3
0
0
0
4
2
I
II
α
β
α
β
Type(II) = A
2
2
0
0
3
3
5
2
I
II
α
β
α
β
Type(II) = B
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View Full Document Question
•
In general, do all preBayesian games
have at least one ex post equilibrium?
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This document was uploaded on 01/05/2012.
 Fall '09

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