Proving the Existence of Stable Assignments in Democratic Forking Using Isabelle/HOL
Résumé
We consider a recent game theory paper, on democratic forking: suppose you want to go to the opera with a group of 10 friends, with a choice of two operas. Everyone has a preference for one of the operas, but everyone also prefers a large community over a small one. Is there an assignment of each friend to one opera that is stable? The paper answers the question affirmatively giving an algorithm.
We have formalised the main result of that paper in the proof assistant Isabelle. This provides proofs of the results that are much more reliable, since computer-checked, than paper-and-pencil proofs. The exercise has also been useful for improving the paper-and-pencil proof. We also contribute some results concerning the uniqueness of assignments.
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