Multi-type Resource Allocation with Partial Preferences

Partial preferences are natural in such problems since the number of bundles grows exponentially We propose multi-type probabilistic serial (MPS) with the number of types, and it is often unreasonable to expect and multi-type random priority (MRP) as extensions agents to form complete preferences over all bundles. of the well known PS and RP mechanisms Unfortunately, it is well known that no mechanism which to the multi-type resource allocation problem assigns each item fully to a single agent satisfies the basic (MTRA) with partial preferences. In our setting, fairness property of equal treatment of equals, meaning that there are multiple types of divisible items, everything else being equal, agents with the same preferences and a group of agents who have partial order should receive the same share of the resources. For example, preferences over bundles consisting of one item whenever two agents have equal and strict preferences over of each type. We show that for the unrestricted items, it is easy to see that no such mechanism satisfies equal domain of partial order preferences, no mechanism treatment of equals.