Building up social capital in a changing world

This paper models the dynamic process through which a large society may succeed in building up its 'social capital' by establishing a stable and dense pattern of interaction among its members. In the model, agents interact according to a collection of (idyosincratic) infinitely repeated Prisoner's Dilemma played on the existing social network. This network not only specifies the playing partners but, crucially, also determines how relevant strategic information diffuses or new cooperation opportunities are found. Over time, the underlying payoffs randomly change, i.e. display some 'volatility'. In response to it, agents react by creating new links and removing others. This combines into a complex but ergodic dynamic process, whose analysis is undertaken in different ways. First, we rely on its ergodicity to 'compute' numerically its long-run regularities. Second, we use mean-field approximations to derive analytical results. Both routes are found in accord and also complementary. The long-run dynamics of the process sharply depends on environmental volatility, displaying the following features: (a) Only if volatility is not too high can the society sustain a dense social network and thus attain a large average payoff. (b) The social architecture endogenously responds to increased volatility by becoming more cohesive. (c) Network-based strategic effects are an essential buffer that preclude the abrupt collapse of the social network in the face of growing volatility. These conclusions are largely in tune with the points stressed in the social-capital literature.