Matching with property rights: an application to Korean teacher transfer program

I model a teacher transfer program in South Korea as a matching-with-contracts problem. The current (non-centralized) system allows a teacher wishing to make an inter-state transfer to submit, at most, one application and will approve only a one-to-one exchange. Consequently, not only is this current system unstable and inefficient, but it also does not adequately reflect the teachers’ preferences. In contrast, the centralized mechanism I propose fully represents teachers’ preferences and is less wasteful. One key requirement of a teacher transfer program is that it must protect the rights of currently existing teachers who wish to transfer from their current positions, perhaps to satisfy familial needs, for only a short period of time. However, as I demonstrate, no stable mechanism exists that guarantee protection for the rights of such teachers to the positions they currently occupy. To solve this problem, I introduce a novel concept called a claim contract. A claim contract, in a matching-with-contracts model, protects current teachers by removing contracts that do not match the specified duration set by these teachers from the set of potential matches. In this paper, I propose a new mechanism, based on a claim contract, that is strategy-proof and approximates stable matching.