Predictive Game Theory
David Wolpert
Computational Sciences Division
NASA Ames Research Center
Wednesday, November 2, 2005
4:30 - 5:45 PM
Terman Engineering Center, Room 453
Abstract:
Conventional noncooperative game theory hypothesizes that
the joint strategy of a set of reasoning players in a game will
necessarily satisfy an "equilibrium concept". All other joint
strategies are considered impossible. Under this hypothesis the only
issue is what equilibrium concept is "correct".
This hypothesis violates the first-principles arguments underlying
probability theory. Indeed, probability theory renders moot the
controversy over what equilibrium concept is correct - every joint
strategy can arise with non-zero probability. Rather than a
first-principles derivation of an equilibrium concept, game theory
requires a first-principles derivation of a distribution over joint
strategies. If one wishes to distill such a distribution down to the
prediction of a single joint strategy, that prediction should be set
by decision theory. Accordingly for any fixed game, the predicted
joint strategy - one's "equilibrium concept" - will vary with the loss
function of the external scientist making the prediction. Game theory
based on such considerations is called Predictive Game Theory (PGT).
This talk shows how information theory provides a distribution over
joint strategies. The connection of this distribution to the quantal
response equilibrium is elaborated. It is also shown that in many
games, having a probability distribution with support restricted to
Nash equilibria - as stipulated by conventional game theory - is
impossible.
PGT is also used to:
i) Derive an information-theoretic quantification of the degree of
rationality;
ii) Derive bounded rationality as a cost of computation;
iii) Elaborate the close formal relationship between game theory and
statistical physics;
iv) Use this relationship to extend game theory to allow
stochastically varying numbers of players.
Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html