Testing substitutability

@article{Hatfield2012TestingS,
  title={Testing substitutability},
  author={John William Hatfield and Nicole Immorlica and Scott Duke Kominers},
  journal={Games and Economic Behavior},
  year={2012},
  volume={75},
  pages={639-645}
}
We provide an algorithm for testing the substitutability of a length-N preference relation over a set of contracts X in time O(|X| ·N). Access to the preference relation is essential for this result: We show that a substitutability-testing algorithm with access only to an agent’s choice function must make an expected number of queries exponential in |X|. An analogous result obtains when the agent’s preferences are quasilinear in a numeraire and the algorithm has access to the agent’s underlying… CONTINUE READING