Core Membership Computation for Succinct Representations of Coalitional Games

In this paper, I compare and contrast two formal results on the computational complexity of core membership determination in two compact representations of coalitional games. Conitzer and Sandholm [1] proposed the multi-issue representations of coalitional games. This representation attempts to decompose a coalitional games into a set of sub-games. Later, Ieong and Shoham [3] proposed the marginal contribution nets (MC-nets) representation of coalitional games. The MC-nets representation attempts to use boolean logic to reduce the size of the coalitional game representation. In this paper, I compare the core membership results for these two coalitional game representations, discuss their implications, and suggest possible future research directions. In particular, these two papers seem to suggest two seemingly contradictory research directions for the core-membership problem. Conitzer and Sandholm [1] argued that stability concepts like the core for coalitional games should take into account of the computational complexity of finding a beneficial deviation for a particular agent. However, Ieong and Shoham [3] argued that it is important to search for more succinct representations of coalitional games which could overcome the computational hardness of the general core membership problem.