Two Notions of Social Capital

We propose a model that reconciles two aspects of social capital: social capital as reciprocal sharing of favors within a selected group vs. social capital as trust that lubricates transactions in societies. The core assumption is that individuals have productive potentials, e.g. innovations, that can not be put at use autonomously. However, individuals can associate in a club to match productive innovator-implementor dyads among the members. For a given club, allowing one new member has the effect of a) an increased pool of innovations and b) an increased pool of potential implementors. Whether a particular member supports the expansion of the club depends on whether she expects to be an implementor or an innovator. When expansion of membership is decided by vote, both small exclusive clubs and open clubs encompassing the whole society can emerge. The outcome depends both on the voting protocol, on the distribution of innovator and implementor skills, and on the maximal potential club size. Moreover, identical environments may generate multiple equilibrium club sizes. In which of these the society ends up depends on the initial conditions and on the voting protocol.