Wenjun Mei

Dynamic models of appraisal networks explaining collective learning

This paper proposes models of learning process in groups of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

Competitive Propagation: Models, Asymptotic Behavior and Quality-Seeding Games

In this paper we propose a class of propagation models for multiple competing products over a social network. We consider two propagation mechanisms: social conversion and self conversion, corresponding, respectively, to endogenous and exogenous factors. A novel concept, the product-conversion graph, is proposed to characterize the interplay among competing products. According to the chronological order of social and self conversions, we develop two Markov-chain models and, based on the independence approximation, we approximate them with two corresponding difference equations systems. Our theoretical analysis on these two approximated models reveals the dependency of their asymptotic behavior on the structures of both the product-conversion graph and the social network, as well as the initial condition. In addition to the theoretical work, we investigate via numerical analysis the accuracy of the independence approximation and the asymptotic behavior of the Markov-chain model, for the case where social conversion occurs before self conversion. Finally, we propose two classes of games based on the competitive propagation model: the one-shot game and the dynamic infinite-horizon game. We characterize the quality-seeding trade-off for the first game and the Nash equilibrium in both games.

On the dynamics of deterministic epidemic propagation over networks

Abstract In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for Susceptible-Infected (SI), Susceptible-Infected-Susceptible (SIS), and Susceptible-Infected-Recovered (SIR) settings. In each setting, we provide a comprehensive nonlinear analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions. For the network SI setting, specific contributions include establishing its equilibria, stability, and positivity properties. For the network SIS setting, we review a well-known deterministic model, provide novel results on the computation and characterization of the endemic state (when the system is above the epidemic threshold), and present alternative proofs for some of its properties. Finally, for the network SIR setting, we propose novel results for transient behavior, threshold conditions, stability properties, and asymptotic convergence. These results are analogous to those well-known for the scalar case. In addition, we provide a novel iterative algorithm to compute the asymptotic state of the network SIR system.

Sequential decision aggregation with social pressure

This paper proposes and characterizes a sequential decision aggregation system consisting of agents performing binary sequential hypothesis testing and a fusion center which collects the individual decisions and reaches the global decision according to some threshold rule. Individual decision makers’ behaviors in the system are influenced by other decision makers, through a model for social pressure; our notion of social pressure is proportional to the ratio of individual decision makers who have already made the decisions. For our proposed model, we obtain the following results: First, we derive a recursive expression for the probabilities of making the correct and wrong global decisions as a function of time, system size, and the global decision threshold. The expression is based on the individual decision makers’ decision probabilities and does not rely on the specific individual decision-making policy. Second, we discuss two specific threshold rules: the fastest rule and the majority rule. By means of a mean-field analysis, we relate the asymptotic performance of the fusion center, as the system size tends to infinity, to the individual decision makers’ decision probability sequence. In addition to theoretical analysis, simulation work is conducted to discuss the speed/accuracy tradeoffs for different threshold rules.