Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 − 1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of Θ( n/k) on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to com- * Author affiliations and emails: W. pute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.

We develop a framework for continuous search for information on a choice set of multiple alternatives, and apply it to consumer search in a product market. When a consumer considers purchasing a product in a product category, the consumer can gather information sequentially on several products. At each moment the consumer can choose which product to gather more information on, and whether to stop gathering information and purchase one of the products, or to exit the market with no purchase. Given costly information gathering, consumers end up not gathering complete information on all the products, and need to make decisions under imperfect information. Under the assumption of constant informativeness of search, we solve for the optimal search, switch, and purchase or exit behavior in such a setting, which is characterized by an optimal consideration set and a purchase threshold structure. The paper shows that a product is only considered for search or purchase if it has a sufficiently high expected utility. Given multiple products in the consumer's consideration set, the consumer only stops searching for information and purchases a product if the difference between the expected utilities of the top two products is greater than some threshold. Comparative statics show that negative information correlation among products widens the purchase threshold, and so does an increase in the number of the choices. Under our rational consumer model, we show that choice overload can occur when consumers search or evaluate multiple alternatives before making a purchase decision. We also find that it is optimal for a monopolistic seller of multiple products to facilitate information search for low-valuation consumers, while obfuscate information for those with high valuations.

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We consider a large decentralized freelance platform where buyers with private information about their quality preferences are matched with freelancers that differ in quality. When posting their job requests, buyers can report their quality preferences via cheap talk, which influences freelancers’ application and pricing strategies. By exaggerating one’s quality preference, a buyer attracts not only more applications from freelancers, but also those with higher quality, at the cost of a higher expected price. We find that it is always an equilibrium for the buyers to report their quality preferences truthfully when they cannot renegotiate with freelancers on their asking prices after getting matched. On the other hand, when postmatch renegotiation is allowed and buyers have relatively high bargaining power, low-type buyers may strategically exaggerate their quality preferences, and subsequently after getting matched, costly signal their true type and bargain for lower prices. From a platform design perspective, our analysis implies that the option of renegotiation, designed to facilitate postmatch information transmission, may backfire by giving rise to buyers’ prematch opportunistic behaviors of information distortion. This paper was accepted by Joshua Gans, business strategy.