Players may act jointly to honor a contract that binds them. Cooperative games afford opportunities for joint action, that is, collective action that is causally coordinated by, say, an agreement among the players. For example, bargainers may reach an agreement about a sale price to coordinate their acts. In coalitional games players may form coalitions of individuals who act jointly. A core allocation gives each coalition at least as much as it can obtain on its own. Some coalitional games have no core allocation, however. Hence collective rationality does not require the players in such games to realize a core allocation. A strong Nash equilibrium is such that no coalition has an incentive to deviate from it. Not all coalitional games have a strong Nash equilibrium, so collective rationality does not impose a general requirement to realize one.
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