Reciprocity-driven Sparse Network Formation

A resource exchange network is considered, where exchanges among nodes are based on reciprocity. Peers receive from the network an amount of resources commensurate with their contribution. We assume the network is fully connected, and impose sparsity constraints on peer interactions. Finding the sparsest exchanges that achieve a desired level of reciprocity is in general NP-hard. To capture near-optimal allocations, we introduce variants of the Eisenberg-Gale convex program with sparsity penalties. We derive decentralized algorithms, whereby peers approximately compute the sparsest allocations, by reweighted l1 minimization. The algorithms implement new proportional-response dynamics, with nonlinear pricing. The trade-off between sparsity and reciprocity and the properties of graphs induced by sparse exchanges are examined.Comment: 19 page

Strategies in social network formation

We run a computerised experiment of network formation where all connections are beneficial and only direct links are costly. Players simultaneously submit link proposals; a connection is made only when both players involved agree. We use both simulated and experimentally generated data to test the determinants of individual behaviour in network formation. We find that approximately 40% of the network formation strategies adopted by the experimental subjects can be accounted for as best responses. We test whether subjects follow alternative patterns of behaviour and in particular if they: propose links to those from whom they have received link proposals in the previous round; propose links to those who have the largest number of direct connections. We find that together with best response behaviour, these strategies explain approximately 75% of the observed choices. We estimate individual propensities to adopt each of these strategies, controlling for group effects. Finally we estimate a mixture model to highlight the proportion of each type of decision maker in the population

Inequality and Network Formation Games

This paper addresses the matter of inequality in network formation games. We employ a quantity that we are calling the Nash Inequality Ratio (NIR), defined as the maximal ratio between the highest and lowest costs incurred to individual agents in a Nash equilibrium strategy, to characterize the extent to which inequality is possible in equilibrium. We give tight upper bounds on the NIR for the network formation games of Fabrikant et al. (PODC '03) and Ehsani et al. (SPAA '11). With respect to the relationship between equality and social efficiency, we show that, contrary to common expectations, efficiency does not necessarily come at the expense of increased inequality.Comment: 27 pages. 4 figures. Accepted to Internet Mathematics (2014

Stochastic network formation and homophily

This is a chapter of the forthcoming Oxford Handbook on the Economics of Networks

Network Formation and Cooperation

In this paper we adopt Granovetter's view expressed in his famous article ''Economic Action and Social Structure: The Problem of Embeddedness'' , where he argues that the concept of man in economics is extremely undersocialized because it ignores the importance of social networks. In so doing the incentives to mutual cooperation in social matching games in which the social network is endogenously determined are studied. The main result shows that in atomized societies where there is no information flows between different pairs of individuals and the rest of the society, individuals choose either to form the maximal number of links possible or to form no links. Whereas in embedded societies where information transmission is allowed, the type of social networks that arise take different architectures some of them symmetric and some of the asymmetric. This allows us to improve our understanding of a wide variety of phenomena as occupational mobility, informal credit markets in rural areas, cooperative formation, social capital, segmented labor markets, international trade and so on. In partricular, the model results are used to explain the concept of social capital , its benefits and costsnetwork Formation, Cooperation, Social Capital

On mesogranulation, network formation and supergranulation

We present arguments which show that in all likelihood mesogranulation is not a true scale of solar convection but the combination of the effects of both highly energetic granules, which give birth to strong positive divergences (SPDs) among which we find exploders, and averaging effects of data processing. The important role played by SPDs in horizontal velocity fields appears in the spectra of these fields where the scale $\sim$4 Mm is most energetic; we illustrate the effect of averaging with a one-dimensional toy model which shows how two independent non-moving (but evolving) structures can be transformed into a single moving structure when time and space resolution are degraded. The role of SPDs in the formation of the photospheric network is shown by computing the advection of floating corks by the granular flow. The coincidence of the network bright points distribution and that of the corks is remarkable. We conclude with the possibility that supergranulation is not a proper scale of convection but the result of a large-scale instability of the granular flow, which manifests itself through a correlation of the flows generated by SPDs.Comment: 10 pages, 11 figures, to appear in Astronomy and Astrophysic

Effort and synergies in network formation

The aim of this paper is to understand the interactions between productive effort and the creation of synergies that are the sources of technological collaboration agreements, agglomeration, social stratification, etc. We model this interaction in a way that allows us to characterize how agents devote resources to both activities. This permits a fullfledged equilibrium/welfare analysis of network formation with endogenous investment efforts and to derive unambiguous comparative statics results. In spite of its parsimony that ensures tractability, the model retains enough richness to replicate a (relatively) broad range of empirical regularities displayed by social and economic networks, and is directly estimable to recover is structural parameters