A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the linear. Each players has a quadratic functional on its own disposal, which should be minimized. case where weight matrices in control costs one player are singular both functionals studied. Hence, under consideration singular. novel definition Nash equilibrium this (a sequence) proposed. solved by appl...

In this paper, we present a numerical method for computing a Nash solution to a zero-sum differential game for a general nonlinear system based on a sequential linearquadratic approximations. The technique is used to design a game-theoretic controller. Numerical results are given which show the performance of the method as well as the performance of the resulting controller under noisy observat...

Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In this survey, we present an overview of the many brands of deterministic dynamical systems motivated by evolutionary game theory, including ordinary differential equations (and, in particular, the repl...

In this paper we review some recent results on non-cooperative and semicooperative differential games. For the n-person non-cooperative games in one-space dimension, we consider the Nash equilibrium solutions. When the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic, we show that the weak solution of a corresponding system of hyperbolic conservation laws deter...

*Correspondence: [email protected] School of Mathematics, Shandong University, Shanda South Road, Jinan, 250100, P.R. China Abstract This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a maximum principle and a verification theorem for the Nash equilibrium poin...

Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an N-person game in which each player has two pure strategies. From the Nash-Tognoli Theorem it follows that every compact differentiable manifold can be encoded as the set of totally mixed Nash equilibria of some game. Moreove...

We formally incorporate the option to gather information into a game and thus endogenize the information structure. We ask whether models with exogenous information structures are robust with respect to this endogenization. Any Nash equilibrium of the game with information acquisition induces a Nash equilibrium in the corresponding game with an exogenous structure. We provide sufficient conditi...

A finite time multi-persons linear-quadratic differential game (LQDG) with bounded disturbances and uncertainties is considered. When players cannot measure these disturbances and uncertainties, the standard feedback Nash strategies are shown to yield to an "-(or quasi) Nash equilibrium depending on an uncertainty upper bound that confirms the robustness property of such standard strategies. In...