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This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…
This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best…
We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time…
In this article, a game-theoretic model is constructed that is related to the problem of optimal assignments. Examples are considered. A compromise point is found, the Nash equilibriums and the decision of the Nash arbitration scheme are…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic…
In this paper, we study closed-loop strong equilibrium strategies for the time-inconsistent control problem with higher-order moments formulated by [Wang et al. SIAM J. Control. Optim., 63 (2025), 1560--1589]. Since time-inconsistency makes…
Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a…
We exhibit optimal control strategies for a simple toy problem in which the underlying dynamics depend on a parameter that is initially unknown and must be learned. We consider a cost function posed over a finite time interval, in contrast…
We consider a scheduling game on parallel related machines, in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to…
We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is…
We study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known…
We introduce the problem of groundwater trading, capturing the emergent groundwater market setups among stakeholders in a given groundwater basin. The agents optimize their production, taking into account their available water rights, the…
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…
The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population…
A Stochastic Control Problem can be solved by Dynamic Programming or Distributed Optimal Control with the Kolmogorov equation for the probability density of the Markov process of the problem. It can be solved also with Supervised Learning.…
We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these…