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On The Decomposability Of Fractional Allocations, Shurojit Chatterji, Peng Liu
On The Decomposability Of Fractional Allocations, Shurojit Chatterji, Peng Liu
Research Collection School Of Economics
A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.
On The Decomposability Of Fractional Allocations, Shurojit Chatterji, Peng Liu
On The Decomposability Of Fractional Allocations, Shurojit Chatterji, Peng Liu
SMU Economics and Statistics Working Paper Series
A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.