On blocking mechanisms in economies with club goods

The paper investigates some classical results concerning the core and competitive equilibria in an economy consisting of both private and club goods, where club goods are treated as articles of choice just like private goods. Clubs in this framework are described by the characteristic of their members and the local project the club endorses. The space of economic agents in our economy is described by a measure space of agents which includes both negligible and non-negligible agents. The competitive equilibria notion in our setup is known as the club equilibria. In this paper, we establish three results: (i) equivalence between the core (resp. club equilibria) of a mixed economy with the core (resp. club equilibria) of its associated continuum economy, which extends the classical core-equivalence theorem of Ellickson et al. \cite{Ellickson et al} to the case of a mixed economy; (ii) extensions of Schmeidler's theorem (refer to \cite{Schmeidler : 72}) and Vind's theorem (refer to \cite{Vind : 72}) to a club economy with a mixed measure space of agents, which provides a sharper characterization of club equilibrium states; and (iii) characterizations of club equilibria in a mixed economy by considering the veto power of the grand coalition in infinitely many economies obtained by perturbation of initial endowments in the original economy.