The Spread of Free-Riding Behavior in a Social Network

We study a model where agents, located in a social network, decide whether to exert effort or not in experimenting with a new technology (or acquiring a new skill, innovating, etc.). We assume that agents have strong incentives to free ride on their neighbors' effort decisions. In the static version of the model efforts are chosen simultaneously. In equilibrium, agents exerting effort are never connected with each other and all other agents are connected with at least one agent exerting effort. We propose a mean-field dynamics in which agents choose in each period the best response to the last period's decisions of their neighbors. We characterize the equilibrium of such a dynamics and show how the pattern of free riders in the network depends on properties of the connectivity distribution.free ride, independent set, local public good, mean field, social network.

Influence networks

Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that the new behavior will easily spread in the population if there is a high correlation between how influential (visible) and how easily influenced an agent is, which is determined by the sampling process and the adoption rule. We also analyze how the density and variance of the out-degree distribution affect the diffusion threshold and the endemic state.social influence, networks, diffusion threshold, endemic state

Diffusion and Contagion in Networks with Heterogeneous Agents and Homophily

We study how a behavior (an idea, buying a product, having a disease, adopting a cultural fad or a technology) spreads among agents in an a social network that exhibits segregation or homophily (the tendency of agents to associate with others similar to themselves). Individuals are distinguished by their types (e.g., race, gender, age, wealth, religion, profession, etc.) which, together with biased interaction patterns, induce heterogeneous rates of adoption. We identify the conditions under which a behavior diffuses and becomes persistent in the population. These conditions relate to the level of homophily in a society, the underlying proclivities of various types for adoption or infection, as well as how each type interacts with its own type. In particular, we show that homophily can facilitate diffusion from a small initial seed of adopters.Comment: 18 pages, 1 figur

Influence networks

Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process, that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the behavior of the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that an increase in the correlation between the out-degree (information level) and in-degree (visibility level) of agents may favor or harm diffusion; the effect actually depends on the specific details of the adoption process

Influence networks

Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that the new behavior will easily spread in the population if there is a high correlation between how influential (visible) and how easily influenced an agent is, which is determined by the sampling process and the adoption rule. We also analyze how the density and variance of the out-degree distribution affect the diffusion threshold and the endemic state

Public goods in directed networks

We study the provision of a public good in a social network where links are directed, i.e., the information flows one way. Our results relate, through stochastic dominance, the equilibrium outcome of such a process with the out-degree distribution of the network

On discrimination in the optimal management of teams

We study the optimal management of teams in which agents’ effort decisions are mapped (via a production technology) into the probability of the team’s success. Optimal wage schemes in such context are largely discriminatory, but we show that the extent of the discrimination crucially depends on the existence of moral hazard. More precisely, for teams with a flat structure, the domain of production technologies giving rise to discrimination is broader when agents’ actions are observable and contractible. For teams with a sequential structure, the result reverses and the domain of production technologies giving rise to discrimination is broader when there exists moral hazard. Finally, in more cooperative environments in which agents are allowed to collude, optimality does not entail discrimination, with or without moral hazard

The principal's dilemma.

A recurrent dilemma in team management is to select between a team-based and an individual based wage scheme. We explore such a dilemma in a simple model of production in teams, in which the team members may di?er in their e?ort choices and quali?cation. We show that, in spite of enhancing output as the basis for payment, a team-based wage scheme might be less pro?table for the principal than an individual-based wage scheme. We also highlight a deep misalignment between designing optimal (output-based) incentives for a team and treating its members impartially. Finally, upon introducing the possibility of liquidity constraints in our model, we provide rationale for the so-called ?rich get richer? hypothesis

To mix or not to mix? Diffusion in groups

The outbreak of epidemics, the rise of religious radicalization, or the motivational influence of fellow students in classrooms are some of the issues that can be described as diffusion processes in heterogeneous groups. Understanding the role that interaction patterns such as homophily, or segregation, play in the diffusion of certain traits or behaviors is a major challenge for contemporary societies. Here, we study the effects on diffusion processes of mixing (or segregating) two different groups –one group that is more sensitive or prone to “infection”, and the other which is more resistant –. We find non-monotonic effects of mixing, and Pareto inefficient segregation levels, e.g., situations where an increase in mixing can benefit both groups. These findings have fundamental consequences for the design of inclusion policies