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We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order "coefficient"…

Here we present a decomposition technique for a class of differential games. The technique consists in a decomposition of the target set which produces, for geometrical reasons, a decomposition in the dimensionality of the problem. Using…

In this paper, a hierarchical one-leader-multi-followers game for a class of continuous-time nonlinear systems with disturbance is investigated by a novel policy iteration reinforcement learning technique in which, the game model consists…

We study a stochastic differential game in a ruin theoretic environment. In our setting two insurers compete for market share, which is represented by a joint performance functional. Consequently, one of the insurers strives to maximize it,…

It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between…

Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…

This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living…

We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…

Cyber deception is one of the key approaches used to mislead attackers by hiding or providing inaccurate system information. There are two main factors limiting the real-world application of existing cyber deception approaches. The first…

This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…

Advanced persistent threats (APT) combine a variety of different attack forms ranging from social engineering to technical exploits. The diversity and usual stealthiness of APT turns them into a central problem of contemporary practical…

A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…

Dynamic game theory is an increasingly popular tool for modeling multi-agent, e.g. human-robot, interactions. Game-theoretic models presume that each agent wishes to minimize a private cost function that depends on others' actions. These…

This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation…

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…

Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…

Textile drying is a key operation in the textile production cycle as it represents one of the most energy-intensive stages and plays a critical role in determining both product quality and overall process efficiency. In this work we propose…

Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks…

This paper constructs a novel intellectual property (IP) protection strategy using differential equation theory, aiming to analyze and optimize the effectiveness of IP protection. By developing a mathematical model, it explores the dynamic…

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…