Predictive Game Theory

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 (mixed) strategies. If you wish to distill such a distribution down to the prediction of a single joint strategy, that prediction should be set by decision theory, using your (!) loss function. 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 can provide such 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.