ABSTRACT

The Shapley value of a two-sided assignment game may not lie in the core. A sufficient condition for the Shapley value of an assignment game to be a core allocation (Hoffman, M.; Sudhölter, P. (2007) The Shapley value of exact assignment games, International Journal of Game Theory, 35, 557-568.) is that the game is exact, that is to say, each coalition attains its worth at some core allocation. This condition is also necessary for some subclasses of assignment markets, such as assortative markets and Böhm-Bawerk markets. This chapter also shows that, for any assignment game, there exists a unique assignment game with individual reservation values that is exact and has the same core. Then, it can be associated with each assignment market the Shapley value of its unique exact representative, and this will always be a core allocation. Moreover, this chapter reviews the axiomatic characterization of the Shapley value on the domain of assignment games provided in van den Brink and Pintér (2015) (Brink van den, R.; Pintér, M. (2015) On axiomatizations of the Shapley value for assignment games, Journal of Mathematical Economics, 60, 110-114.). This axiomatization relies on two properties: submarket efficiency and valuation fairness.