Assignment Games with Externalities - Jens Gudmundsson; Helga Habis (Lund University, School of Economics and Management, Department of Economics, 2013)
We introduce externalities into a two-sided, one-to-one assignment game by letting the values generated by pairs depend on the behavior of the other agents. Extending the notion of blocking to this setup is not straightforward; a pair has to take into account the possible reaction of the residual agents to be able to assess the value it could achieve. We define blocking in a rather general way that allows for many behavioral considerations or beliefs. The main result of the paper is that a stable outcome in an assignment game with externalities always exists if and only if all pairs are pessimistic regarding the others' reaction following a deviation. The relationship of stability and optimality is also discussed, as is the structure of the set of stable outcomes.
Keywords: C71; C78; D62; 330; Two-sided matching; assignment game; externalities; stability