Coordination without Common Knowledge: Separating First- and Higher-Order Belief Failures

Abstract

We study coordination when the rules and payoffs of the game are common knowledge, but recognition of the efficient focal action is not. In such environments, a subject who recognizes the focal action may still fail to coordinate on it either because she doubts that her opponent also recognizes it, or because she doubts that this recognition is sufficiently shared. We adapt the five-sector-disc environment of Blume and Gneezy (2010) and add a Prediction task to a Self task and a Coordination task. The self task identifies recognition types. The prediction task identifies whether a recognizer’s first-order belief about the opponent’s type crosses the relevant threshold. The coordination game then reveals whether coordination failure remains once this first-order threshold is crossed.

The design provides a choice-based identification strategy for separating coordination failure due to low first-order beliefs from failure due to higher-order beliefs, without directly eliciting beliefs. In the data, 75 of 130 subjects are classified as high-recognition types. Among them, 57 choose the distinct sector throughout, 7 fail due to first-order beliefs, and another 7 fail only due to higher-order beliefs. Thus efficient coordination is common even without common knowledge of recognition types, but half of the failures cannot be reduced to first-order pessimism. The results show that higher-order doubt affects coordination behavior in a simple laboratory environment without explicit incentives for recursive reasoning.