Conference Agenda

In this work we study a class of stationary mean-field games (MFGs) of singular stochastic control under Knightian uncertainty. The representative agent adjusts the dynamics of an Itô-diffusion via a one-sided singular stochastic control and faces a long-time-average expected profit criterion. The mean-field interaction is of scalar type and it is given through the stationary distribution of the population. Due to the presence of ambiguity, the problem of representative agent constructed as a stochastic (zero-sum) game. The decision maker chooses the 'best' policy and the adverse player the 'worst' probability measure. Via a constructive approach, we prove the existence and uniqueness of the stationary mean-field equilibrium. Finally, we provide a case study to illustrate the impact of uncertainty to the mean field equilibria. This is a joint work with Giorgio Ferrari.

This paper examines finite-player incomplete information games where players may hold mutually inconsistent beliefs without requiring a common prior. Within a framework where the action space is compact metrizable and the type space is Polish, players' beliefs are assumed to be absolutely continuous with respect to a product measure. We consider an auxiliary complete information game with a common prior and show that a Bayesian equilibrium exists in the original game if and only if a Nash equilibrium exists in the auxiliary game. This equivalence provides a way for establishing the existence of Bayesian equilibria across a broad class of games, including those with action-discontinuous payoffs. Additionally, through this equivalence, established existence results such as Balder (1988) and Carbonell-Nicolau and McLean (2018) can be leveraged to demonstrate equilibrium existence in particular cases. The framework is applied to analyze games with large type spaces which accommodate infinite belief hierarchies, demonstrating the existence of equilibria in such settings.