_:nb5731901d4d2415a8b16d33f2d7b21f3xb0
<http://schema.org/description>
"For the class of vertex cover games (introduced by Deng et al., Math. Oper.\nRes., 24:751-766, 1999), we investigate the population monotonic allocation\nschemes (introduced by Sprumont, Games Econ. Behav., 2: 378-394, 1990). We\npresent a complete characterization for the class of vertex cover games\nadmitting a population monotonic allocation scheme (PMAS for short), i.e., a\nvertex cover game has a PMAS if and only if the underlying graph is\n(K_3,C_4,P_5)-free. Our characterization implies that the existence of a\nPMAS can be determined efficiently for vertex cover games. We also propose an\nalternative description for PMAS-es in vertex cover games based on the dual\nlinear program of the vertex cover problem, which reveals the dual-based\nallocation scheme nature of PMAS-es. Moreover, we give a complete\ncharacterization for integral PMAS-es in vertex cover games via stable\nmatchings and show that the celebrated Gale-Shapley algorithm (introduced by\nGale and Shapley, Amer. Math. Monthly, 69:9-15, 1962) can be used to produce\nall integral PMAS-es in vertex cover games."
<https://deepai.org/publication/population-monotonic-allocation-schemes-for-vertex-cover-games>