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 (shapley and shubik (1972)) and the class of component additive games (curiel et al. (1994)). We first present some elementary features of neighbor games. After that we provide a polynomially bounded algorithm of order p 3 for calculating the leximax solution (cf. Arin and iñarra (1997)) of neighbor games, where p is the number of players.