Cognitive Hierarchy in Capacity Allocation Games

Forthcoming, Management Science

50 Pages Posted: 20 Oct 2015 Last revised: 30 Dec 2016

See all articles by Tony Haitao Cui

Tony Haitao Cui

University of Minnesota - Twin Cities

Yinghao Zhang

University of Cincinnati

Date Written: February 8, 2016


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.

Keywords: capacity allocation, cognitive hierarchy, strategic thinking, behavioral operations management, behavioral economics

Suggested Citation

Cui, Tony Haitao and Zhang, Yinghao, Cognitive Hierarchy in Capacity Allocation Games (February 8, 2016). Forthcoming, Management Science, Available at SSRN: or

Tony Haitao Cui

University of Minnesota - Twin Cities ( email )

321 19th Ave S
Suite 3-150
Minneapolis, MN 55455
United States

Yinghao Zhang (Contact Author)

University of Cincinnati ( email )

2529 Campus Green Dr.
Cincinnati, OH 45221
United States

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