The Core of Games with Stackelberg Leaders

This paper considers cooperative game theoretic settings in which forming coalitions can act as Stackelberg leaders. We de�fine a value function which modi�fies 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 defi�ne what we call the phi-core, and characterize the phi-core allocations of a cartel formation game and of a public goods economy.