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This paper considers cooperative game theoretic settings in which forming coalitions can act as Stackelberg leaders. We define a value function which modifies the gamma-value function (Hart & Kurz, 1983, Chander & Tulkens, 1997) by letting members of deviating coalitions move first in choosing a coordinated strategy. We accordingly define what we call the phi-core, and characterize the phi-core allocations of a cartel formation game and of a public goods economy.

A Sequential Approach to the Characteristic Function and the Core in Games with Externalities