2016 Theses Doctoral

# Pricing Models in the Presence of Informational and Social Externalities

This thesis studies three game theoretic models of pricing, in which a seller is interested in optimally pricing and allocating her product or service to a market of agents, in order to maximize her revenue. These markets feature a large number of self-interested agents, who are generally heterogeneous with respect to some payoff relevant feature, e.g., willingness to pay when agents are consumers or private cost when agents are firms. Agents strategically interact with one another, and their actions affect other agents' payoffs, either directly through social influence or competition, or indirectly through a review system. The seller has demand uncertainty and strives to optimize expected discounted revenues. I use either a mean-field approximation or a continuum of agents assumption to reduce the complexity of the problems and provide crisp characterizations of system aggregates and equilibrium policies.

Chapter 2 considers the problem of an information provider who sells information products, such as demand forecasts, to a market of firms that compete with one another in a downstream market. We propose a general model that subsumes both price and quantity competition as special cases. We characterize the optimal selling strategy and find that it depends on both mode and intensity of competition. Several important extensions to heterogeneous production costs, information quality discrimination, and information leakage through aggregate actions are studied.

Chapter 3 considers the problem of optimally extracting a stream of revenues from a sequence of consumers, who have heterogeneous willingness to pay and uncertainty about the quality of the product being sold. Using an intuitive maximum likelihood procedure, we characterize the solution of consumers' quality estimation problem. Then, we use a mean-field approximation to characterize the transient dynamics of quality estimates and demand. These allow us to simplify and solve the monopolist's problem, and ultimately provide a characterization of her optimal pricing policy.

Chapter 4 considers the problem of a seller who is interested in dynamically pricing her product when consumers' utility is influenced by the mass of consumers that have purchased in the past. Two scenarios are studied, one in which the monopolist has commitment power and one in which she does not. We characterize the optimal selling strategy under both scenarios and derive comparisons on equilibrium prices and demands. Our main result is a characterization of the value of price commitment as a function of the social influence level in the market.

## Files

- Crapis_columbia_0054D_13431.pdf binary/octet-stream 1.23 MB Download File

## More About This Work

- Academic Units
- Business
- Thesis Advisors
- Maglaras, Constantinos
- Degree
- Ph.D., Columbia University
- Published Here
- June 27, 2016