Robust Predictions under Finite Depth of Reasoning

When players have a finite depth of reasoning, it is usually assumed that each player has a commonly known anchor behavior. This paper provides a general framework to examine whether predictions are robust to uncertainty about other players' anchors. We give two different sufficient conditions for the robustness. The first condition shows that any p-dominant equilibrium is robust if players put sufficiently small probability (decreasing in p) on high-depth types. This result highlights a distinction between two prominent finite depth of reasoning models: a risk dominated equilibrium is robust in the cognitive hierarchy model, but not in the level-k model. We also show that equilibria of dominance solvable models are robust.