# Poster session and reception

Tuesday, May 15, 2018 - 4:30pm - 6:00pm

Lind 400

**Value of Price Discrimination in Large Random Networks**

Jiali Huang (University of Minnesota, Twin Cities)

We study the value of price discrimination in large random networks. Recent trends in industry suggest that increasingly firms are using information about social network to offer personalized prices to individuals based upon their positions in the social network. In the presence of positive network externalities, firms aim to increase their profits by offering discounts to influential individuals that can stimulate consumption by other individuals at a higher price. However, the lack of transparency in discriminative pricing can reduce consumer satisfaction and create mistrust. Recent research has focused on the computation of optimal prices in deterministic networks under positive externalities. We would like to answer the question: how valuable is such discriminative pricing? We find, surprisingly, that the value of such pricing policies (increase in profits due to price discrimination) in very large random networks are often not significant. We provide the exact rates at which this value grows in the size of the random networks for different ranges of network densities.**Coffee Shop Operations with Mobile Ordering**

Kang Kang (University of Minnesota, Twin Cities)

Mobile ordering is becoming popular in the world of coffee shop, fast food or restaurants. Our work examines the operations of a coffee shop where some customers can use a mobile app to skip the ordering and payment queue. Using queueing theory, we explore the impact of mobile customers on walk-in customers and vice versa across a variety of service policies.**Stochastic Network Modeling of Financial Systemic Risk**

David Yao (Columbia University)

We demonstrate how stochastic networks can be an effective modeling tool for studying defaults and contagion dynamics in a financial system. Specifically, this can be accomplished via formulating a high dimensional dynamic complementarity problem, also known as the Skorohod problem. An algorithm that solves the Skorohod problem will generate all possible default times over any given horizon, along with the evolution dynamics of each bank's asset values, liabilities and payment flows. The results will inform the development of new risk measures for default clustering and contagion concentration.**Stochastically modeled reaction networks: Positive recurrence and mixing times**

Jinsu Kim (University of Wisconsin, Madison)

Reaction networks are graphical configurations that can be used to describe biological interaction networks. If the abundances of the constituent species of the system are low, we can model the dynamics of species counts in a jump by jump fashion as a continuous time Markov chain. In this talk, we will mainly focus on which conditions of the graph imply positive recurrence (existence of a stationary distribution) for the associated continuous time Markov chain. I will also present results related to their mixing times, which give the time required for the distribution of the continuous time Markov chain to get close to the stationary distribution.