Cost Allocation

Game Theory · Axiom Academy

How game theory helps fairly split costs in shared infrastructure ✈ The Classic Airport Runway Problem Imagine three airlines sharing an airport. They need runways of different lengths based on their aircraft: Small planes: Need a 1,000m runway (costs 1M to build) Medium planes: Need a 2,000m runway (costs 3M to build) Large planes: Need a 3,000m runway (costs 5M to build) The challenge: If they build one 3,000m runway for 5M, how should the three airlines split the cost fairly? Why this matters: This same problem appears everywhere—utilities sharing power grids, cities sharing water treatment plants, companies sharing fiber optic cables, and more! Several approaches might seem reasonable at first: Each airline pays: 5M ÷ 3 = 1.67M Problem: Small planes only need 1M of runway! Small: 1M, Medium: 3M, Large: 5M Problem: Total = 9M but runway only costs 5M! Small: 1M, Medium: 2M, Large: 2M Better, but doesn't account for cooperation benefits! Uses cooperative game theory to find the fairest split! Accounts for all possible coalitions! Before we reveal the Shapley value solution, consider this: Which airline benefits the most from cooperation? Think about who saves the most money by sharing instead of building their own runway. The Shapley value fairly allocates costs by considering every possible order in which players could join the coalition, then averaging their marginal contributions.

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