Approximate core allocations for edge cover games

Abstract

Edge cover games are cooperative cost games arising from edge cover problems. In an edge cover game, each player controls a vertex and the cost of a coalition is the minimum weight of edge covers in the subgraph induced by the coalition. The approximate core is a relaxation of the core which is one of the most important concepts in cooperative game theory. A vector belongs to the α-core (0≤α≤1) if it recovers at least α-fraction of the total cost of the game when no deviating coalition is better off. In this paper, we show that the 34-core of edge cover games is always non-empty and a vector in the 34-core can be computed efficiently. We also show that 34 is the best constant ratio for the approximate core of edge cover games, as it is the reciprocal of the integrality gap for edge cover problems.