Vilius Žukauskas

Vilius Žukauskas completed his doctorate at the Faculty of Mathematics and Informatics of Vilnius University, where his dissertation studied Nash equilibria in N-player stochastic differential games with finite and infinite horizon objectives. The central results established existence and uniqueness of Nash equilibria in a class of stochastic games where each player's state evolves as a diffusion process influenced by the controls of all other players, and characterised the equilibrium value functions as viscosity solutions of a coupled system of Hamilton-Jacobi-Isaacs equations. The dissertation also addressed the convergence of N-player equilibria to their mean field limits as N grows large — establishing propagation of chaos estimates and quantifying the rate at which the N-player Nash equilibrium approaches the solution of the corresponding mean field game system. He subsequently held a postdoctoral fellowship at the Department of Mathematics of Stockholm University, where he worked on ergodic properties of stochastic differential games and the long-time behaviour of equilibrium distributions.

His subsequent research examined zero-sum stochastic differential games under partial observation, where neither player has access to the full state of the system and both must form optimal strategies based on filtered information. This required combining the theory of partially observed stochastic control — with its associated filtering equations and belief-state formulation — with the two-player adversarial structure of the Hamilton-Jacobi-Isaacs framework. A complementary line of work addressed the ergodic problem for stochastic differential games, establishing conditions under which long-run average payoff criteria admit stationary equilibria and characterising these through coupled ergodic HJI equations whose analysis differs substantially from the finite-horizon case.

At IADU, Žukauskas contributes stochastic games theory to the Institute's research programme on multi-agent policy problems and optimal regulatory design. His work examines the structure of Nash and saddle-point equilibria in stochastic differential game formulations of sovereign policy problems — including competitive monetary policy, strategic debt management, and regulator-institution adversarial models — and the relationship between N-player stochastic game equilibria and their mean field game counterparts in settings where individual agent anonymity holds approximately but not exactly.