Game Theory Course: 2.2 Iterated Dominance and Rationalizability

Jim Ratliff

Game Theory

Nonequilibrium Solution Concepts

Article

By assuming that the players' rationality is common knowledge, we can justify an iterative process of outcome rejection--the iterated elimination of strictly dominated strategies--which can often sharpen our predictions. Outcomes which do not survive this process of elimination cannot plausibly be played when the rationality of the players is common knowledge. A similar, and weakly stronger, process--the iterated elimination of strategies which are never best responses--leads to the solution concept of rationalizability. The surviving outcomes of this process constitute the set of rationalizable outcomes. Each such outcome is a plausible result (and these are the only plausible results)when the players' rationality is common knowledge. In two-player games the set of rationalizable outcomes is exactly the set of outcomes which survive the iterated elimination of strictly dominated strategies. In three-or-more-player games, the set of rationalizable outcomes can be strictly smaller than the set of outcomes which survives the iterated elimination of strictly dominated strategies.