  For vertex cover games (introduced by Deng et al., Math. Oper. Res.,
24:751-766, 1999), we investigate population monotonic allocation schemes
(introduced by Sprumont, Games Econ. Behav., 2: 378-394, 1990). 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, Amer. Math.
Monthly, 69:9-15, 1962).
