search-s

search-s - Mediators Slides by Sherwin Doroudi Adapted from...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Mediators Slides by Sherwin Doroudi Adapted from “Mediators in Position Auctions” by Itai Ashlagi, Dov Monderer, and Moshe Tennenholtz
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Bayesian & Pre-Bayesian 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”)
Background image of page 2
Bayesian & Pre-Bayesian 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)
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Bayesian & Pre-Bayesian Games In a pre-Bayesian 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
Background image of page 4
Equilibria in Pre-Bayesian Games When priors regarding types are not known (i.e. in pre-Bayesian 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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Ex: Pre-Bayesian 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
Background image of page 6
Ex: Pre-Bayesian 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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Question In general, do all pre-Bayesian games have at least one ex post equilibrium?
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 01/05/2012.

Page1 / 30

search-s - Mediators Slides by Sherwin Doroudi Adapted from...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online