Before revision: Efficiency and fairness are two desiderata in market design . Fairness requires randomization in many environments. As one of the few successful matching mechanisms, Top Trading Cycle (TTC) is well known for being efficient to solve deterministic allocation problems. But it is inadequate to incorporate randomization efficiently and fairly. We propose a class of Fractional TTC mechanisms to solve random allocation problems efficiently and fairly. Dropping the graph-based definition of TTC , we use parameterized linear equations to describe how agents trade endowments or priorities at each step.
After revision: Efficiency and fairness are two desiderata in market design environments. Dropping the traditional idea of clearing cycles in generated graphs , we use parameterized linear equations to describe how agents trade endowments or priorities at each step.