"Fictitious Play for a Continuum of Anonymous Players"

Speaker: Zinovi Rabinovich, University of Southampton
Date: Wednesday, 27 May 2009
Time: 3pm
Place: Ross 201

Abstract:

The Fictitious Play (FP) algorithm was developed in 1951 by Brown to
find an approximate Nash equilibrium for zero sum games. Since then,
however, the algorithm has been successfully extended and applied to
an ever increasing variety of games. In this talk I will present an
extension of the FP algorithm that can be used in games with a
Continuum of Anonymous Players (CAPs). These games are characterized
by two properties. First, the utility of a player depends only on the
set of actions applied by its opponents, but not on which opponent
played which action. Second, the (virtual) number of opponents a
player is facing is so large, that they form a continuum. Both of
these properties are found in auction settings and, in fact, CAPs
formally model almost all types of auctions with a continuous private
value. Therefore, an auction setting was selected as a natural
candidate to test our extended FP version. Specifically, the algorithm
was applied to simultaneous auctions to obtain new results on the Nash
equilibrium of this type of auctions.