Social loss with respect to the core of an economy with externalities

We consider a pure exchange economy with externalities. We adopt a cooperative approach to equilibrium analysis, allowing each individual to cooperate with others and to form coalitions. Individual preferences are affected by the consumption of all other agents in the economy, and the consumption set of each agent is affected by the coalition to which he/she belongs. Following Montesano (Soc Choice Welf 19:763–767, 2002), we introduce a measure of social loss with respect to the γ-core and α-core of the economy which completely characterizes the corresponding core allocations