Coalitional Control and the Core with Consumption Externalities

We introduce a family of core notions for pure exchange economies with consumption externalities by separating the coalition whose members benefit from a deviation from the economic domain through which the deviation is implemented. Each nonempty beneficiary coalition S is associated with a control set A_S, which determines both the consumption positions that may be modified and the resources available to the deviation. The framework accommodates self control, Berge type complement control, and intermediate control structures. We study the efficiency and resource properties of the associated cores and provide conditions under which they coincide with the set of Pareto optimal allocations. We also examine how changes in the control correspondence affect blocking power and core inclusion, obtaining implications for existence results. For a class of network economies, we characterize core allocations and show that changing control rights can restore non-emptiness when the self-regarding core is empty. Finally, we introduce a pessimistic version of the core, in which beneficiaries must improve under every feasible redistribution outside the control domain, and establish corresponding results on efficiency, resource characterization, and control expansion.