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This paper introduces the formalism required to analyze a certain class of stochastic control problems that involve a super diffusion as the underlying controlled system. To establish the existence of these processes, we show that they are…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a…
We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on…
We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a…
Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal…
This paper focuses on a class of continuous-time controlled Markov chains with time-inconsistent and distribution-dependent cost functional (in some appropriate sense). A new definition of time-inconsistent distribution-dependent…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the…
A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense…
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function…
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of…
In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…
A solution concept that is a refinement of Nash equilibria selects for each finite game a nonempty collection of closed and connected subsets of Nash equilibria as solutions. We impose three axioms for such solution concepts. The axiom of…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…
The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading…
In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best…