This article studies a leader–follower differential game with finite horizon, where single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that user demand fully satisfied (that is, interior solution considered), and following different tariff schemes are analyzed: linear scheme, increasing block tariff, convex t...

Fluid models of queueing networks are important for the development of optimal service strategies. Nonnegativity constraints on the state variables lead to discontinuous dynamics, often modeled using the “Skorokhod problem” formulation. These dynamics in a classical robust L2-gain control formulation lead to a differential game with some unusual features. In simple examples the differential gam...

This paper is motivated by certain ideas which arise in the theory of differential games (see [3, 41). We abstract the particular features of differential games which are relevant in the notion of a positional game. Suppose S is a topological space, and g is a continuous real-valued function on S. We consider a game between two players, whom we call the maximizer and the minimizer, which falls ...

In an earlier study, presented at the 3 rd EUCASS [1], an innovative guidance strategy was outlined by integrating the design of a multiple model adaptive estimator and a differential game based guidance law. Such strategy indicated two potential breakthroughs in the interception of randomly maneuvering targets in Ballistic Missile Defense. Further studies indicated that while the differential ...

We consider a population of “crowd-averse” dynamic agents controlling their states towards regions of low density. This represents a typical dissensus behavior in opinion dynamics. Assuming a quadratic density distribution, we first introduce a mean-field game formulation of the problem, and then we turn the game into a two-point boundary value problem. Such a result has a value in that it turn...

A pursuit-evasion differential game of countably many pursuers and one evader is investigated. Integral constraints are imposed on the control functions players. Duration fixed, payoff functional greater lower bound distances between when completed. The want to minimize, maximize payoff. In this paper, we find value construct optimal strategies for

The paper is concerned with an n-person differential game in one space dimension. We state conditions for which the system of Hamilton–Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the nonc...