Related papers: Game theory with integral equations as state dynam…
We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
This paper formulates and studies a linear quadratic (LQ for short) game problem governed by linear stochastic Volterra integral equation. Sufficient and necessary condition of the existence of saddle points for this problem are derived. As…
We develop an Integral Transformation Method (ITM) for the study of suitable optimal control and differential game models. This allows for a solution to such dynamic problems to be found through solving a family of optimization problems…
Game theory provides a framework for studying communication dynamics and emergent phenomena arising from rational agent interactions. We present a model framework for the Volunteer's Dilemma with four key contributions: (1) formulating it…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…
This work uses game theory as a mathematical framework to address interaction modeling in multi-agent motion forecasting and control. Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces…
We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
The game theory techniques are used to find the equilibrium of a market. Game theory refers to the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents,…
The application of the methods of quantum mechanics to game theory provides us with the ability to achieve results not otherwise possible. Both linear superpositions of actions and entanglement between the players' moves can be exploited.…
We formulate and analyze a hybrid system model that involves Volterra integral operators with multiple integrals and two types of impulsive terms. We give a constructive proof, via an iteration method, of existence and uniqueness of…
We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional…
We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and second players are, respectively, to minimize and maximize a…
In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our…
Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
We present a game-theoretic perspective on the problems of quantum state estimation and quantum cloning. This enables us to show why the focus on universal machines and the different measures of success, as employed in previous works, are…
Evolutionary game theory is a mathematical toolkit to analyse the interactions that an individual agent has in a population and how the composition of strategies in this population evolves over time. While it can provide neat solutions to…