Shapley Meets Lakoff: Construction Cost Allocation Aligns with Social Status in the Case of Skyscrapers

We examine the fair allocation of the construction costs among the buyers of units located on different stories of a building. The rationale for the diverse allocation of the costs is two fold: from a supply perspective, the higher the story is, the greater the inflexibility it imposes on the entrepreneur due to the accompanying commitment to build all stories underneath; from a demand viewpoint, it follows from Lakoff (1980) that, because of inherent cognitive motives, agents commonly prefer higher stories to lower ones, ceteris paribus. Relying on cooperative game theory analysis, we thus propose an applied theoretical mechanism that fairly allocates the construction costs among the stories of the building. This mechanism is based on the Shapley value approach. We further develop a relative social status function and show that the latter both conforms to a series of reasonable axioms and is consistent with the attained Shapley solution. Essentially, under the attained solution, each story’s share in the total construction cost rises in a particular way with its vertical location in the building. We further derive closed-form and simulated properties of the suggested cost allocation. *The Arison School of Business, The Interdisciplinary Center Herzliya; P.O. Box 167, Herzliya 46150, Israel; telefax: +972-9-952-7298, fax: +972-9-956-8605, email: [email protected] **The Arison School of Business, The Interdisciplinary Center Herzliya; P.O. Box 167, Herzliya 46150, Israel; telefax: +972-9-952-7307, fax: +972-9-956-8605, email: [email protected] #We would like to thank Chen Alon and the participants of the Economics Department seminar at the Chinese University of Hong Kong for helpful comments.