Cognitive hierarchy in capacity allocation games

We examine a supply chain with a single supplier and multiple retailers to predict retailers' actual ordering behaviors. If retailer orders exceed supplier capacity, a proportional rationing rule applies to capacity allocation among retailers. We propose a behavior model based on cognitive hierarchy theory, in which retailers with different levels of strategic-reasoning capabilities form heterogeneous beliefs about other players' capabilities when choosing their orders. This behavioral model yields three interesting predictions. First, retailers' orders increase as the number of retailers decreases or the supplier's production capacity shrinks. Second, the orders tend to increase as the retailer population becomes more "sophisticated." Third, retailers' profits first increase in relation to their strategic-reasoning capabilities and then decrease, indicating an inverted U-shaped relationship between profits and strategic-reasoning capabilities. We experimentally examine the capacity allocation game with participants motivated by financial incentives. The experimental results and structural model estimation confirm the predictions of the behavioral model.