How to use decision theory to choose among mechanisms
We extend a recently introduced approach to the positive problem of game theory, Predictive Game Theory (PGT Wolpert (2008)). In PGT, modeling a game results in a probability distribution over possible behavior proﬁles. This contrasts with the conventional approach where modeling a game results in an equilibrium set of possible behavior proﬁles. We analyze three PGT models. Two of these are based on the well-known quantal response and epsilon equilibrium concepts, while the third is entirely new to the economics literature. We use a Cournot game to demonstrate how to use our extension of PGT, concentrating on model combination, modeler uncertainty, and mechanism design. In particular, we emphasize how PGT allows a modeler to perform prediction and mechanism design in a manner that is fully consistent with decision theory. We do this even in situations where conventional approaches yield multiple equilibria, an ability that is necessary for a fully decision theoretic mechanism design. Where possible, PGT results are compared against equilibrium set analogs.