David H. Wolpert (NASA Ames)
STATISTICAL PREDICTION OF THE OUTCOME OF A NONCOOPERATIVE GAME
6 October 2008, 3:30-5pm
The Institute of Mathematical Sciences, Imperial College London, 53
Prince's Gate, South Kensington, London SW7 2PG
This seminar is jointly organised by the Statistical Computing Section
of the Royal Statistical Society, the Institute for Mathematical
Sciences (Imperial College London) and the ALADDIN project
(www.aladdinproject.org <outbind://186/www.aladdinproject.org> ).
Registration is recommended. To register, please email Marcia Salviato
([log in to unmask]). Note that that seminar is free and open to
all. Directions to the venue are available from
http://www3.imperial.ac.uk/mathsinstitute/contacts
<http://www3.imperial.ac.uk/mathsinstitute/contacts>
http://www3.imperial.ac.uk/pls/portallive/docs/1/32853696.PDF
<http://www3.imperial.ac.uk/pls/portallive/docs/1/32853696.PDF>
(building 19) http://www3.imperial.ac.uk/campusinfo/
<http://www3.imperial.ac.uk/campusinfo/>
For further information, please contact Niall Adams
([log in to unmask]).
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STATISTICAL PREDICTION OF THE OUTCOME OF A NONCOOPERATIVE GAME
David H. Wolpert
NASA Ames Research Center
MS 269-2
Moffet Field, CA 94035, USA
[log in to unmask]
ti.arc.nasa.gov/people/dhw
Abstract:
Many statistics problems involve predicting the joint strategy that will
be chosen by the players in a noncooperative game. Conventional game
theory predicts that the joint strategy will satisfy an ``equilibrium
concept''. The relative probabilities of the joint strategies satisfying
the equilibrium concept are not given, and all joint strategies that do
not satisfy it are given probability zero.
As an alternative, I view the prediction problem as one of statistical
inference, where the ``data'' includes the details of the noncooperative
game. This replaces conventional game theory's focus on how to specify a
set of equilibrium joint strategies with a focus on how to specify a
density function over joint strategies.
I explore a Bayesian version of such a Predictive Game Theory (PGT) that
provides a posterior density over joint strategies. It is based on the
the entropic prior and on a likelihood that quantifies the rationalities
of the players.
The Quantal Response Equilibrium (QRE) is a popular game theory
equilibrium concept parameterized by player rationalities. I show that
for some games the local peaks of the posterior density over joint
strategies approximate the associated QRE's, and derive the associated
correction terms. I also discuss how to estimate parameters of the
likelihood from observational data, and how to sample from the
posterior. I end by showing how PGT can be used to specify a
{\it{unique}} equilibrium for any noncooperative game, thereby providing
a solution to a long-standing problem of conventional game theory.
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