Neighbor games and the leximax solution

Neighbor games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, the class of neighbor games is the intersection of the class of assignment games and the class of component additive games. We first present some elementary features of neighbor games. After that we provide a polynomially bounded algorithm of order p³ for calculating the leximax solution of neighbor games, where p is the number of players.