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• A payoff vector (ai)i S is said to be feasible for a coalition S if and only if
• A payoff vector (ai)i S is said to be individually rational if and only if
This states that cooperation guarantees to each layer at lease what he/she can secure
alone.
• Collective rationality. For any coalition in other words, no
utility is lost.
• Pareto Optimality. This axiom means that no agent can improve her own utility
without hurting somebody else,
In what follows, we will rely on two major approaches, considered fair, to pin down
plausible solutions which satisfy the three above conditions. First, solutions have to be
fair to both partners; in which case, we will discuss the core (Gillies, 1953), as a fair
solution. Second, solutions have to also exhibit fairness, in this regard, we will the
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and
discuss applications of the Shapley value (Shapley, 1953).
5. The Core
The core of a cooperative game is an outcome of cooperation which provides enough
incentives for the agents to remain within the grand coalition. In other words, the core is a
setting which is able to sustain a stable cooperation. The core is a set of efficient
allocations from a coalition that based on the notion of stability. To every transferable
utility game, the core assigns a set such as:
This condition above states that no coalition S could better on its own by deviating from
the grand coalition N. In other words, the core solution is stable when all players in the
grand coalition gain imputations greater than their stand alone payoffs, v(S).