Depth of Reasoning and Information Revelation: An Experiment on the Distribution of k-Levels

The level-k model is a workhorse in behavioral game theory. For comparisons across experiments and predictions in future studies, it is crucial to assess the empirical distribution of k-levels. We present a revelation game suitable for this purpose. In a labor market context, workers can choose to reveal their productivity at a cost, and players’ strategies reveal their level of reasoning in terms of a k-level. We find that the most frequently observed reasoning levels are k = 2 and k = 3. In our game roughly 30% of the players are k ≤ 1 and 25% are k ≥ 4. We compare our results to other experiments that identify level-k distribution, foremost to the money request (or 11–20) game. Despite various differences to the 11–20 game, our revelation game suggests a very similar distribution of level-k types.