Seminars

In this talk, a new framework for modeling and solving mathematical games will be introduced. As a collection of interdependent decision problems, games can be thought of as a network of mathematical programs, where the network connectivity characterizes the information pattern of the game. We refer to these networks as Mathematical Program Networks. The MPN framework naturally encompasses common continuous game formulations such as Nash equilibrium problems, Stackelberg/bilevel equilibrium problems, and multi-leader-multi-follower games. However the power in thinking of games as MPNs lies in the ability to represent and solve new types of problems which otherwise don’t fit into the common templates. 

In practical applications of game theory, choosing a model for the information pattern characterizing the relationship between different decision-makers is not always easy. Different choices may lead to drastically different equilibrium solutions. From a computation perspective, different choices of information pattern may also require different algorithms to find solutions. The motivation for the presented work is to provide a framework which allows treating the information pattern of a game as a modeling choice, just like the cost and constraint functions of the constituent decision problems are modeling choices. Within the MPN framework, the information pattern can be altered and the resulting equilibrium points can be compared with ease.

This talk will cover both theoretical and practical implications of the MPN framework, and considerable time will be spent discussion important subclass of MPNs. When the decision problems constituting a MPN are each Quadratic Programs, we say that the resulting network is a Quadratic Program Network, or a QPN. Despite the restrictions placed on the constituent decision problems, these QPNs remain very expressive and admit some desirable properties which can be exploited to develop a fairly simple algorithm for finding equilibrium points of the network. This algorithm will be described, and its efficacy will be shown on a few interesting examples. 

Bio: Dr. Forrest Laine is an Assistant Professor in the Computer Science and Mechanical Engineering departments at Vanderbilt University, where he directs the Vanderbilt Mathematical Programming and Intelligent Robotics (VAMPIR) Lab. He received his Ph.D. from UC Berkeley in 2021, and previously worked at various companies in the Autonomous Vehicle industry.