Core theory for multiple-sided assignment games (Q1913575)

In 1972 Shapley and Shubik introduced the \(n\)-person cooperative games known as the assignment games. They have two types of players (buyers and sellers) and the coalitional value of any one buyer with one seller is given. The core of a game consists of all payoffs to the players that cannot be improved upon by any coalition, and it is always a nonempty set. When assignment games are extended to three or more different types of players the core may be empty. This paper describes some characterizations for nonempty cores and the probabilities of this occurring for some classes of these multi-sided assignment games.