Economic Models in MFG and Related Topics - Part 1

Registration to attend is essential. Please contact Dr Alpár Mészáros, Mathematical Sciences (alpar.r.meszaros@durham.ac.uk) or Dr Mauro Bambi, Economics (mauro.bambi@durham.ac.uk)

Schedule

• 10:00 -10:50
  Professor Ronnie Sircar (Princeton University)
  
  
  Title: Stochastic Games of Intensity Control
  
  
  Abstract
  We discuss some mean field games of stochastic intensity control with applications to income inequality, cryptocurrency mining and ticket pricing.  For the latter problem, one way to capture both the elastic and stochastic reaction of purchases to price is through a model where sellers control the intensity of a counting process, representing the number of sales thus far. The intensity describes the probabilistic likelihood of a sale, and is a decreasing function of the price a seller sets. A classical model for ticket pricing, which assumes a single seller and  infinite time horizon, is by Gallego and van Ryzin (1994) and it has been widely utilized by airlines, for instance. Extending to more realistic settings where there are multiple sellers, with finite inventories,  in competition over a finite time horizon is more complicated both mathematically and computationally. We discuss a dynamic mean field game of this type, and some numerical and existence-uniqueness results.
  
  

• 11:00-11:50 
  Dr Bar Light (National University of Singapore)
  
  
  Title: Uniqueness, Computing, and Learning Mean Field Equilibria with Scalar Interactions: Theory and Applications
  
  
  Abstract
  Mean field equilibrium (MFE) has become a powerful solution concept for analyzing large dynamic games, offering computational tractability in a variety of settings. However, computing MFE poses significant challenges due to nonlinearities and the absence of contraction properties, which hinder its use for   credible counterfactual analysis and reliable comparative statics. This paper studies MFE in dynamic models where players interact through a scalar function of the population distribution, referred to as the scalar interaction function. These models naturally arise in diverse applications, including dynamic oligopoly models such quality ladder models, online marketplaces, and heterogeneous-agent macro models. We present novel iterative algorithms that leverage the structure of scalar interactions to compute MFE under mild assumptions. Unlike existing methods, our algorithms do not require monotonicity or contraction properties, substantially expanding their applicability. Additionally, we propose a model-free algorithm that utilizes reinforcement learning techniques, including Q-learning and policy gradient methods, to learn MFE without requiring prior knowledge of payoff or transition functions. We establish finite-time performance bounds for this algorithm under Lipschitz continuity assumptions. Our framework demonstrates its versatility through applications to dynamic competition models, such as capacity and inventory competition, as well as online marketplaces, including ridesharing and dynamic reputation systems. Furthermore, we establish conditions for the uniqueness  of equilibrium leveraging monotonicity conditions. We use our algorithms to derive comparative statics in various models to analyze the influence of market design parameters on equilibrium outcomes.
  
  

• 14:00-14:50
  Sebastial Merkel (University of Bristol)
  
  
  Title: Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models
  
  
  Abstract
  We propose and compare new global solution algorithms for continuous time heterogeneous agent economies with aggregate shocks. First, we approximate the agent distribution so that equilibrium in the economy can be characterized by a high, but finite, dimensional non-linear partial differential equation. We consider different approximations: discretizing the number of agents, discretizing the agent state variables, and projecting the distribution onto a finite set of basis functions. Second, we represent the value function using a neural network and train it to solve the differential equation using deep learning tools. The main advantage of this technique is that it allows us to find global solutions to high dimensional, non-linear problems. We demonstrate our algorithm by solving versions of important models in the macroeconomics and spatial literatures (e.g. Krusell and Smith (1998), Khan and Thomas (2007), Bilal (2023), Kaplan and Violante (2014)). The talk is based on a joint work with Zhouzhou Gu, Mathieu Lauriere and Jonathan Payne.