A Robust Information Source Estimator with Sparse Observations

In this paper, we consider the problem of locating the information source with sparse observations. We assume that a piece of information spreads in a network following a heterogeneous susceptible-infected-recovered (SIR) model and that a small subset of infected nodes are reported, from which we need to find the source of the information. We adopt the sample path based estimator developed in [1], and prove that on infinite trees, the sample path based estimator is a Jordan infection center with respect to the set of observed infected nodes. In other words, the sample path based estimator minimizes the maximum distance to observed infected nodes. We further prove that the distance between the estimator and the actual source is upper bounded by a constant independent of the number of infected nodes with a high probability on infinite trees. Our simulations on tree networks and real world networks show that the sample path based estimator is closer to the actual source than several other algorithms

Essays on Internet economics: customer reviews, advertising, and technology adoption

This dissertation consists of three chapters on the economics of the Internet. The first chapter begins with presenting the advertising spending patterns of US local restaurants that have different ratings on Yelp.com. Rating information on Yelp includes display ratings and review distributions. The Yelp's rounding algorithm creates a discontinuity in display ratings. Therefore, I use a regression discontinuity design to identify the effect of a higher display rating on local restaurants' advertising spendings. I find a significantly negative effect of display rating for highly-rated restaurants on advertising. However, when the display rating is constant between two steps, the relationship between local restaurant advertising spending and average rating is significantly positive. The second chapter uses a game-theoretic model to analyze competing firms' advertising and pricing decisions. Here customer reviews are available and firms may build up loyal customer bases. I find that highly-rated firms are more likely to advertise more, i.e., online reviews complement advertising. Comparative static results can explain the results found in the first chapter. Intuitively, when the capacity of a local business becomes limited, a jump in the display rating will reduce the complementary effect of online reviews on advertising. I also analyze an extension of the model, where an entrant and an incumbent interact. I find that customer reviews undo the "fat-cat" effect of a large incumbent with lots of loyal customers. The third chapter proposes a new explanation for adoption failure or delay in markets with network effects. In the model, consumers and software providers play a dynamic adoption game. Each group of players choose between two incompatible technologies. Consumers may wait, but firms may not. Although efficiency requires one technology to be adopted by all consumers and firms right away, there is a "market split and adoption delay" equilibrium. In this equilibrium some consumers choose to wait at first and firms split between the two technologies. The model is motivated by the 56K modem market, in which competition between two technologies appears to have led to adoption failure, until an industry standard setting organization coordinated the market on an alternative standard