Matching and the Allocation of Indivisible Objects Via Deferred Acceptance under Responsive Preferences

It is well-known that economics is the science of allocating scarce resources. Often this is done using money as our daily shopping routines confirm. Sometimes, there is more to the allocation mechanism than simple price setting and taking, but even auction mechanisms as encountered on e-bay are now well accepted rationing mechanisms. However, there are economic problems in which using money and prices to match resources and consumers is not usually done or is considered immoral or even illegal. Examples for this type of problems are the assignments of students to public schools or universities or the assignment of transplant organs to patients who urgently need these transplants. If money cannot or should not be used to determine who gets what, how else can we decide on matching resources to consumers