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Shapley Cost Allocation Coincides with Relative Status: The Case of Skyscrapers

Danny Ben-Shahar, Yongheng Deng, and Eyal Sulganik
Empirical evidence shows that the value of units in a building generally rises with their floor level due to features such as the better view and lesser noise experienced in higher stories. We adopt a theoretical approach for examining the value of units in different floors based on the allocation of land and construction cost among the stories of the building. Relying on cooperative game theory analysis, we propose the Shapley value approach as a mechanism for allocating these costs. We examine the allocation mechanism and derive several closed-form properties by which the value pattern of stories in a building is rationalized. Furthermore, following Lakoff and Johnson (1980), we argue that agents achieve greater status from occupying higher stories because of inherent cognitive motives. We thus constitute the Relative L&J Status function and formally show that its properties coincide with those of the difference between the costs allocated to any two stories in the building, thereby, derive a new property to the Shapley solution. Finally, we empirically test the derived Shapley cost allocation properties and the attained results are consistent with our major predictions.