We study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems that show that when the signals observed by the players satisfy a condition known as (ǫ, γ)-differential privacy, that the folk theorem has little bite: for values of ǫ and γ sufficiently small, for a fixed discount factor, any equilibrium of the repeated game involve players playing appr...

This paper studies two non-zero-sum stochastic differential games of control and stopping. One game has interaction in the players’ stopping rules, whereas the other does not. Solutions to backward stochastic differential equations (BSDEs) will be shown to provide the value processes of the first game. A multi-dimensional BSDE with reflecting barrier is studied in two cases for its solution: ex...

Location estimation of mobile target is an important research in wireless sensor networks. However, the phenomenon of non line of sight affects the accuracy of location estimating algorithms greatly. In order to improve the accuracy of location estimation of mobile targets, we proposed a game theory based location method algorithm in wireless sensor networks. In the proposed method, we first es...

We present a novel trajectory optimization framework to address the issue of robustness, scalability and efficiency in optimal control and reinforcement learning. Based on prior work in Cooperative Stochastic Differential Game (CSDG) theory, our method performs local trajectory optimization using cooperative controllers. The resulting framework is called Cooperative Game-Differential Dynamic Pr...

A well-known differential game in the theory of differential games is the “homicidal chauffeur” problem which was introduced by Isaacs [7]. It is a pursuit-evasion game. In the paper, a variant of this problem proposed by Bernhard [3] is considered. The computation of level sets of the value function in this variant becomes difficult since holes in the “victory domains” of the pursuer can appea...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.

These notes provide a brief introduction to the theory of noncooperative differential games. After the Introduction, Section 2 reviews the theory of static games. Different concepts of solution are discussed, including Pareto optima, Nash and Stackelberg equilibria, and the co-co (cooperative-competitive) solutions. Section 3 introduces the basic framework of differential games for two players....

abstract a quantitative framework of combination of liner programming and cooperative game theory was used in this study to analyze and model cooperative contracts in production based on rural households' resources cooperation in firoozabad plain. revenues and costs in cooperation game theory have important rule to get agreement. transaction cost function was used in cooperative costs accountin...

We study zero-sum dynamic games with deterministic transitions and alternating moves of the players. Player 1 aims at reaching a terminal set and minimising a running and final cost. We propose and analyse an algorithm that computes the value function of these games extending Dijkstra’s algorithm for shortest paths on graphs. We also show the connection of these games with numerical schemes for...

A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a differential game that can be explicitly solved. While the characterization of the limit by a differential game is akin to results at the large deviation scale, ...