Complexity of Core

Years and Authors of Summarized Original Work

• 2001; Fang, Zhu, Cai, Deng

Problem Definition

The core is one of the most important solution concepts in cooperative game, which is based on the coalition rationality condition: no subgroup of the players will do better if they break away from the joint decision of all players to form their own coalition. The principle behind this condition can be seen as an extension to that of the Nash Equilibrium in noncooperative games. The work of Fang, Zhu, Cai, and Deng [4] discusses the computational complexity problems related to the cores of some cooperative game models arising from combinatorial optimization problems, such as flow games and Steiner tree games.

A cooperative game with side payments is given by the pair (N, v), where N = {1, 2, …, n} is the player set and $v : 2^{N} \rightarrow R$ is the characteristic function. For each coalition $S \subseteq N$, the value v(S) is interpreted as the profit or cost achieved by the...