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. Our mechanisms are ex-ante efficient. They satisfy various fairness axioms when parameters are properly chosen . We apply them to a couple of market design problems and obtain efficient and fair assignments in all of them .
We propose a new method to define trading algorithms in market design environments. Dropping the traditional idea of clearing cycles in generated graphs , we use parameterized linear equations to define trading algorithms. Our method has two advantages. First, our method avoids discussing the details of who trades with whom and how, which can be a difficult question in complex environments. Second, by controlling parameter values in our equations, our method is flexible and transparent to satisfy various fairness criteria . We apply our method to several models and obtain new trading algorithms that are efficient and fair .
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Efficiency and fairness are two desiderata
We propose a new method to define trading algorithms
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. 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
environments. Dropping the traditional idea of clearing cycles in generated graphs
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describe how agents trade endowments or priorities at each step. Our mechanisms are ex-ante efficient. They
define trading algorithms. Our method has two advantages. First, our method avoids discussing the details of who trades with whom and how, which can be a difficult question in complex environments. Second, by controlling parameter values in our equations, our method is flexible and transparent to
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axioms when parameters are properly chosen
criteria
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them to a couple of market design problems and obtain
our method to several models and obtain new trading algorithms that are
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assignments in all of them