Population monotonic allocation schemes for vertex cover games

Abstract

For vertex cover games (introduced by Deng et al. (1999) [2]), we investigate population monotonic allocation schemes (introduced by Sprumont (1990) [11]). We show that the existence of a population monotonic allocation scheme (PMAS for short) for vertex cover games can be determined efficiently and that a PMAS, if exists, can be constructed accordingly. We also show that integral PMAS-es for vertex cover games can be characterized with stable matchings and be enumerated by employing Gale-Shapley algorithm (introduced by Gale and Shapley (1962) [4]).