STABLE SETS IN ECONOMIES WITH CLUB GOODS

3 The first part of the paper analyses whether a correspondence exists between stable sets in a continuum club economy consisting of a finite type of individuals and those that form in the associated club economy containing a finite number of individuals. [...] { ∫ ∫ } Si = t ∈ Ii|f(t) ̸= ξi = fdµ and λ(t) ̸= li = λdµ { ∫ Ii ∫Ii } Pi = t ∈ Ii|f(t) ̸= ξi = fdµ and λ(t) = l = λdµ{ i∫Ii ∫Ii } Qi = t ∈ Ii|f(t) = ξi = fdµ and λ(t) ̸= li = λdµ Ii Ii 15 Let S = {j ∈ 1, ..., n|µ(Sj) > 0}, P = {j ∈ 1, ..., n|µ(Pj) > 0} and Q = {j ∈ 1, ..., n|µ(Qj) > 0}. [...] If GP is payoffs sophisticated stable set in the continuum club economy E, then the corresponding set ∫ ∫ GPF = {(u1(x1, λ1), ..., un(xn, λn)) | xi = fdµ, λi = ldµ and u(f, l) ∈ GP} Ii Ii is a payoffs sophisticated stable set in the finite club economy EF. [...] Conversely, if GPF is a payoffs sophisticated stable set in the finite club economy EF , then the associated set GP = {u(f, l) | f(t) = xi, l(t) = λi ∀t ∈ Ii and (u1(x1, λ1), ..., u Pn(xn, λn)) ∈ GF} is a payoffs sophisticated stable set in the continuum club economy E. [...] Consider the corresponding allocations in the continuum club economy E, (f, l) and (z′, l′) with f(t) = x1, l(t) = λi, z′(t) = zi and l′(t) = νi for all t ∈ Ii and i = 1, ..., n.