scholarly journals Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2170
Author(s):  
Abdulla Azamov ◽  
Gafurjan Ibragimov ◽  
Tolanbay Ibaydullaev ◽  
Idham Arif Alias
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Optimal Number ◽  
Skeleton Graph ◽  
The One

We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
P. CARDALIAGUET ◽  
M. QUINCAMPOIX
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Random Distribution ◽  
Uniqueness Result ◽  
Initial Condition ◽  
Initial State ◽  
Lack Of Information ◽  
In The Beginning ◽  
Zero Sum ◽  
Future Work

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

scholarly journals Evasion-Pursuit Strategy against Defended Aircraft Based on Differential Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qilong Sun ◽  
Minghui Shen ◽  
Xiaolong Gu ◽  
Kang Hou ◽  
Naiming Qi
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Optimal Strategies ◽  
Open Loop ◽  
Active Defense ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
One To One ◽  
The One

The active defense scenario in which the attacker evades from the defender and pursues the target is investigated. In this scenario, the target evades from the attacker, and the defender intercepts the attacker by using the optimal strategies. The evasion and the pursuit boundaries are investigated for the attacker when the three players use the one-to-one optimal guidance laws, which are derived based on differential game theory. It is difficult for the attacker to accomplish the task by using the one-to-one optimal guidance law; thus, a new guidance law is derived. Unlike other papers, in this paper, the accelerations of the target and the defender are unknown to the attacker. The new strategy is derived by linearizing the model along the initial line of sight, and it is obtained based on the open-loop solution form as the closed-loop problem is hard to solve. The results of the guidance performance for the derived guidance law are presented by numerical simulations, and it shows that the attacker can evade the defender and intercept the target successfully by using the proposed strategy.

A TIME-CONSISTENT SOLUTION FORMULA FOR BARGAINING PROBLEM IN DIFFERENTIAL GAMES

2014 ◽  
Vol 16 (04) ◽  
pp. 1450016 ◽  
Author(s):  
LEON A. PETROSYAN ◽  
DAVID W. K. YEUNG
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Bargaining Problem ◽  
Individual Rationality ◽  
Payoff Distribution ◽  
Consistent Solution ◽  
Cooperative Differential Game

This paper presents a solution formula for the payoff distribution procedure of a bargaining problem in cooperative differential game that would lead to a time consistent outcome. In particular, individual rationality is satisfied for every player throughout the cooperation period.

Public holidays, tourism, and economic growth

2017 ◽  
Vol 24 (4) ◽  
pp. 473-485 ◽  
Author(s):  
Franco Barrera ◽  
Nicolás Garrido
Keyword(s):  
Economic Growth ◽  
Optimal Number ◽  
The Other ◽  
Nonlinear Relationship ◽  
Other Hand ◽  
The One ◽  
Public Holidays

In this article, a mechanism supporting the existence of an inverted u-shaped relation between the number of public holidays and the growth of an economy is presented. The nonlinear relationship is originated by two forces within a Schumpeterian economy: On the one hand, as the number of public holidays grows, the total number of workers searching for innovation increases; on the other hand, as the number of days of recreation increases, the number of working days producing innovations decreases. The combination of these two forces generates the inverted u-shaped relationship. The hypothesized mechanism suggests the existence of an optimal number of public holidays for an economy.

scholarly journals A differential game of N persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium

2021 ◽  
Vol 57 ◽  
pp. 104-127
Author(s):  
V.I. Zhukovskii ◽  
Yu.S. Mukhina ◽  
V.E. Romanova
Keyword(s):  
Nash Equilibrium ◽  
Differential Games ◽  
Explicit Form ◽  
Differential Game ◽  
Linear Quadratic ◽  
Equilibrium Situation ◽  
Pareto Equilibrium ◽  
Noncooperative Differential Games

A linear-quadratic positional differential game of N persons is considered. The solution of a game in the form of Nash equilibrium has become widespread in the theory of noncooperative differential games. However, Nash equilibrium can be internally and externally unstable, which is a negative in its practical use. The consequences of such instability could be avoided by using Pareto maximality in a Nash equilibrium situation. But such a coincidence is rather an exotic phenomenon (at least we are aware of only three cases of such coincidence). For this reason, it is proposed to consider the equilibrium of objections and counterobjections. This article establishes the coefficient criteria under which in a differential positional linear-quadratic game of N persons there is Pareto equilibrium of objections and counterobjections and at the same time no Nash equilibrium situation; an explicit form of the solution of the game is obtained.

scholarly journals Linear Programming Optimization Techniques for Addis Ababa Public Bus Transport

2021 ◽  
Author(s):  
Eshetie Berhan ◽  
Daniel Kitaw
Keyword(s):  
Linear Programming ◽  
Addis Ababa ◽  
Optimal Number ◽  
Public Enterprise ◽  
Scheduling System ◽  
Assignment Method ◽  
Bus Scheduling ◽  
Lp Model ◽  
Bus Service ◽  
The One

Anbessa City Bus Service Enterprise (ACBSE) is the only public enterprise that provides transport services in the city of Addis Ababa. The enterprise uses a fixed bus schedule system to serve passengers in more than 125 routes. However, the current bus assignment and scheduling system are becoming a challenge in the company’s operational performances. The objective of this paper is to develop an optimum bus assignment method using linear programming (LP). After a thorough analysis of the existing bus scheduling system, the LP model is developed and used to determine the optimal number of busses for each route in four shifts. The output of the LP-model is then validated with the performances of the existing systems. The findings of the study showed that the new model reveals better performances on the operating costs, bus utilization, and trips and distance covered compared with the existing scheduling system. The bus utilization is improved by the new system and cut costs on the one hand and improves the service quality to passengers on the other hand. The authors recommended the enterprise to adopt the new bus assignment system so that busses can be assigned based on the demand distribution of passengers for each route at a given shift.

scholarly journals Application of Differential Games in Mechatronic Control System

2016 ◽  
Vol 21 (4) ◽  
pp. 867-878 ◽  
Author(s):  
Z. Hendzel ◽  
P. Penar
Keyword(s):  
Game Theory ◽  
Differential Games ◽  
Differential Game ◽  
Approximate Solutions ◽  
Control Problems ◽  
Optimum Control ◽  
Object A ◽  
Differential Game Theory ◽  
Single Link ◽  
Zero Sum

Abstract Differential games are a combination of game theory and optimum control methods. Their solutions are based on Bellman's principle of optimality. In this paper, the zero-sum differential game theory has been used for the purposes of controlling a mechatronic object: a single-link manipulator. In this case, analytical solutions are unavailable, thus approximate solutions were used. Two approximation methods were compared with the use of numerical simulations and selected quality indicators. The results confirm previous assumptions and the connection between the differential game theory and H∞ control problems.

Minimax differential game with delay

2020 ◽  
pp. 359-369
Author(s):  
Arkadii V. Kim ◽  
Gennady A. Bocharov
Keyword(s):  
Dynamic Programming ◽  
Differential Games ◽  
Differential Game ◽  
Programming Method ◽  
Dynamic Programming Method ◽  
Mixed Strategies ◽  
Dimensional Theory ◽  
Analysis Methodology ◽  
Finite Dimensional ◽  
Finite Dimensional Case

The paper considers a minimax positional differential game with aftereffect based on the i-smooth analysis methodology. In the finite-dimensional (ODE) case for a minimax differential game, resolving mixed strategies can be constructed using the dynamic programming method. The report shows that the i-smooth analysis methodology allows one to construct counterstrategies in a completely similar way to the finite-dimensional case. Moreover as it is typical for the use of i-smooth analysis, in the absence of an aftereffect, all the results of the article pass to the corresponding results of the finite-dimensional theory of positional differential games.

scholarly journals Corruption and Deforestation: a differential game model

2016 ◽  
Vol 6 (1) ◽  
pp. 481 ◽  
Author(s):  
Cassandro Mendes ◽  
Sabino Junior
Keyword(s):  
Theoretical Model ◽  
Public Sector ◽  
Differential Games ◽  
Differential Game ◽  
International Institutions ◽  
Game Model ◽  
The Public ◽  
Simple Theoretical Model ◽  
Global Issue ◽  
The Relationship

<p class="ber"><span lang="EN-GB">Deforestation is a global issue and recently has been given much attention by governments and international institutions. The present paper aims to present a simple theoretical model on the relationship between corruption and deforestation. To model such relationship, we used differential games. Our model suggests that corruption increases deforestation. Moreover, the salary paid in the public sector may be an important tool to fight deforestation in development countries.</span></p>

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