Consistency, converse consistency and strategic justifications in the airport problem∗

We study the “airport problem”, which is concerned with sharing the cost of an airstrip among agents who need airstrips of different lengths. We address whether different formulations of consistency and converse consistency axioms provide strategic justifications for different rules. We propose Right-endpoint Subtraction (RS) bilateral consistency and RS converse consistency in the airport problem, and find that the nucleolus satisfies the two properties. We then introduce a 3-stage extensive form game to implement the nucleolus that exploits the properties. As we show, there is a unique subgame perfect equilibrium outcome of the game and moreover, it is the allocation chosen by the nucleolus. Our result together with Hu et al. (2011)’s strategic justification of the constrained equal benefits rule provides a positive answer to the question. Journal of Economic Literature Classification Numbers: C71; C72; D63; D70.