On the Problem of Optimal Fair Exchange
Abstract
Abstract We consider the optimal exchange problem, which can be formulated as a version of the problem of optimal transport for measures. For the optimal exchange problem, we prove the existence of an optimal solution and a duality theorem in the case of completely regular topological spaces. We show a connection between the optimal exchange problem and the problem of optimal transport for measures with a density constraint. Using this connection, we obtain a formula for the optimal value in the optimal exchange problem.
Fields of Study & Subjects
Game Theory and Voting Systems
Auction Theory and Applications
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 3-4
- Pages
- 441–452
- Publication date
- 1 April 2026
- Language
- EN