Building Up Social Capital in a Changing World: A Network Approach

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 infinitely repeated Prisoner’s Dilemmas played on the current 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”, which leads agents to react by creating new links and removing others. The process is ergodic, so we use numerical simulations to “compute” its long-run invariant behavior and obtain the following conclusions: (a) Only if payoff volatility is not too high can the society sustain a dense social network. (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, largely in tune with those of the social-capital literature, are further studied analytically in a companion paper through the use of mean-field techniques.Social Capital, Prisoner's Dilemma, Search, Social Networks, Volatility

Network Organizations

It is common to define a network organization as one that is fast and flexible in adapting to changes in the underlying environment. But besides the short-run advantages of adaptability, fast changes in the structure of the organization can also be detrimental in the longer run. This happens, in particular, because agents need to depend widely on that structure to channel appropriately (and thus speed up) search. I discuss the trade-off between adaptability and structural stability in a changing environment where, if the structure of the organization adjusts, information on the exact nature of the change becomes known only with some lag. The main conclusion obtained is that, as environment becomes more volatile, the optimal mode of the organization sharply switches from being totally flexible to being completely rigid, i.e. no intermediate configurations are essentially ever optimal. This has stark implications on the dichothomy of stability versus change that has been highlighted by recent organization literature.

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.social capital, volatility.

LEARNING, NETWORK FORMATION AND COORDINATION

In many economic and social contexts, individual players choose their partners and also decide on a mode of behavior in interactions with these partners. This paper develops a simple model to examine the interaction between partner choice and individual behavior in games of coordination. An important ingredient of our approach is the way we model partner choice: we suppose that a player can establish ties with other players by investing in costly pair-wise links. We show that individual efforts to balance the costs and benefits of links sharply restrict the range of stable interaction architectures; equilibrium networks are either complete or have the star architecture. Moreover, the process of network formation has powerful effects on individual behavior: if costs of forming links are low then players coordinate on the risk-dominant action, while if costs of forming links are high then they coordinate on the efficient action.Networks, social learning, equilibrium selection

Network Formation and Social Coordination

This paper develops a simple model to examine the interaction between partner choice and individual behavior in games of coordination. An important ingredient of our approach is the way we model partner choice: we suppose that a player can establish ties with other players by unilaterally investing in costly pair-wise links. In this context, individual efforts to balance the costs and benefits of links are shown to lead to a unique equilibrium interaction architecture. The dynamics of network formation, however, has powerful effects on individual behavior: if costs of forming links are below a certain threshold then players coordinate on the risk-dominant action, while if costs are above this threshold then they coordinate on the efficient action. These findings are robust to a variety of modifications in the link formation process. For example, it may be posited that, in order for a link to materialize, the link proposal must be two-sided (i.e. put forward by both agents); or that, in case of a unilateral proposal, the link may be refused by the other party (if, say, the latter's net payoff is negative); or that a pair of agents can play the game even if connected only through indirect links.Networks, Links, Coordination games, Equilibrium selection, Risk dominance, Efficiency

Search and Homophily in Social Networks

We study the formation of social ties among heteogeneous agents in a model where meetings are governed by agents' directed search. The aim is to shed light on the important issue of homophily (the tendency of agents to connect with others of the same type). The essential contribution of the model is to provide a basic microfoundation for the opportunity/meeting biases that, as the literature highlights, are a crucial element of the phenomenon. Under the assumption that search is more effective in large pools, the equilibrium is characterized by a threshold in terms of group size: large groups only search among similar agents while smaller groups search in the whole population. This threshold behavior is consistent with the empirical evidence observed in a range of social environments such as high school friendships and interethnic marriages. And assuming that search is subject to small frictions, it also generates the bell-shaped form of the so-called Coleman index observed in the data. Other implications of the model supported by the evidence concern the pattern of cross-group ties among small groups, the linearity of excess homophily for large groups, and the positive effect on it of overall population size.Homophily, search, social networks, segregation.

Unfolding social hierarchies in large population games

Consider a large (continuum) population of finitely-lived agents organized in hierarchical levels.Every period, agents are matched to play a certain symmetric game. On the basis of the payoffsobtained, a certain p-fraction of those who performed best at each level are promoted upwords. Onthe other hand, newcomers replacing those who die every period enter at the lowest level andimitate unbiasedly (but subject to noise) the actions adopted at the highest one. In this context, the (unique) long-run behavior of the system is fully characterized for the wholeclass of 2x2 coordination games. The results crucially depend on the institutional parameter p(which refelcts how hierarchical - or selective - the society is) and on a purely ordinal criterion onthe payoffs of the game. In particular, efficent (or inefficent behaviour) may prevail in the long run -even when risk-dominated - if promotion in society is (or, respectively, is not) selective enough.Social hierarchies, large population games

COMPETITION AND CULTURE IN THE EVOLUTION OF ECONOMIC BEHAVIOR: A SIMPLE EXAMPLE

Competition tends to promote efficient (equilibrium) behavior through the higher survival of the organizations (say firms) that adopt it. On the other hand, culture (understood as the "inherited" social pattern of behavior) may induce certain short-run inertias. This paper analyzes a dynamic model of the struggle between these two forces in the evolution of alternative stable configurations of an economy's behavior.

SHAPING LONG-RUN EXPECTATIONS IN PROBLEMS OF COORDINATION

When far-sighted agents may adjust their behavior only gradually , the issue of equilibrium selection in games becomes one of tension between "history" and "expectations". This paper analyzes whether, in this context, a planner may intervene successfully through short-run policies which redirect expectations away from the inertia of undesired history. The possibilities and limitations of such approach to "expectation management" are studied in a game-theoretic framework where both the planner and the population are involved in a struggle to impose their (credible) commitment possibilities.