Facility location (cooperative game)

The cooperative facility location game is a cooperative game of cost sharing.

The most socially-desirable outcome of the game is that all agents are served.

The cost of this outcome (8 in the above example) can be shared among the agents.

A cost-allocation is good if no sub-group of agents can deviate and get a lower cost for itself (such cost-allocation is said to be in the core of the game).

In the above example: A classic result in game-theory, the Bondareva–Shapley theorem, gives necessary and sufficient conditions for a game to have nonempty core.