Costly Network Formation and Regular Equilibria

We prove that for generic network-formation games where players incur some strictly positive cost to propose links the number of Nash equilibria is finite. Furthermore all Nash equilibria are regular and, therefore, stable sets.Network-formation games; Regular equilibrium; Stable sets

Collaboration in Social Networks

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria -- that we call "collaborative equilibria" -- that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks

Competing for attention in social communication markets

We investigate the incentives for social communication in the new social media technologies. Three features of online social communication are represented in the model. First, new social media platforms allow for increased connectivity; i.e., they enable sending messages to many more receivers, for the same fixed cost, compared to traditional word of mouth. Second, users contribute content because they derive status- or image-based utility from being listened to by their peers. Third, we capture the role of social differentiation, or how social distance between people affects their preferences for messages. In the model, agents endogenously decide whether to be a sender of information and then compete for the attention of receivers. An important point of this paper is that social communication incentives diminish even as the reach or the span of communication increases. As the span of communication increases, competition between senders for receiver attention becomes more intense, resulting in senders competing with greater equilibrium messaging effort. This in turn leads to lower equilibrium payoffs and the entry of fewer senders. This result provides a strategic rationale for the socalled participation inequality phenomenon, which is a characteristic of many social media platforms. We also show that social differentiation may enhance or deter sender entry depending on whether it can be endogenously influenced by senders. Finally, we examine how the underlying network structure (in terms of its density and its degree distribution) affects communication and uncover a nonmonotonic pattern in that increased connectivity first increases and then reduces the entry of senders

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

Self-Organizing Innovation Networks: When do Small Worlds Emerge?

In this paper, we present a model of 'collective innovation' built upon the network formation formalism. In our model, agents localized on a circle benefit from knowledge flows from other agents with whom they are directly or indirectly connected. They support costs for direct connections which are linearly increasing with geographic distance. The dynamic process of network formation exhibits prefeRential meeting for close agents (in the relational network and in the geographic metrics). We show how the set of stochastically stable networks selected in the long run is affected by the degree of knowledge transferability. We find critical values of this parameter for which stable \"small world\" networks are dynamically selected.Network Formation, Stochastic Stability, Preferential Meeting, Self-Organization,