We consider a problem in which a set of agents have to carry out an enterprise;
if they succeed in performing it they have to pay a cost, but they receive a benefit. In our situation the cost depends on the agents involved, while the benefit is fixed.
We may refer to connection situations where the objective and the benefit is the connection of two different nodes and the cost is the minimum cost connection. Another possibility is represented by several firms that have to produce a machine that is sold at a fixed price; each firm may produce all the components of the machine, but they have different technologies, so that the components have different costs. If a subset of firms agree on a joint production, they can save on the costs, while the selling price remains fixed.
Also bankruptcy situations match our hypotheses with the estate in the role of the fixed benefit, while the costs are the claims of the agents not in the coalition. Finally the model fits insurance situations where a set of companies may reduce the costs if they share the risk, but the amount of the premium is fixed and independent from the number of companies.
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