Mathematical Models Of Conflict Research Articles

Оптимізація стратегій сумісного прийняття рішень операторами аеронавігаційної системи в конфліктних ситуаціях

У статті представлено проблему визначення оптимальних стратегій сумісного прийняття рішень пілотом та авіадиспетчером як задачу розв’язання “конфліктуˮ між ними методами теорії ігор. Наведено приклад моделі конфліктної ситуації “пілот – авіадиспетчерˮ в особливому випадку в польоті “Відмова та пожежа двигуна на повітряному судні при наборі висоти після зльотуˮ. Показано, що в аварійній ситуації за відсутності зв’язку авіадиспетчера з екіпажем повітряного судна, наявності безпілотних повітряних суден та високій завантаженості зони управління повітряним рухом оптимальною стратегією пілота є посадка в автоматичному режимі на аеродромі з підготовленою злітно-посадковою смугою, обладнаному радіотехнічними засобами посадки.

Development of a mathematical model of conflict between the parties in the implementation of the offset transaction

The object of research of this work is the conflict of interests of the parties in the implementation of offset agreements. One of the most problematic places when implementing offset agreements is that a wide variety of sudden events, force majeure circumstances, etc. can take place – phenomena that can’t be described in detail and predicted with acceptable accuracy in full. In addition, the offset contract is a conflict of interest between the seller and the buyer. During the study, the methods of the humanitarian and natural-scientific approach are used, thanks to which the conflict was given a new interpretation. It is considered as a way of interaction of complex systems. It is shown that the conflict is not a synonym for confrontation, but a way to overcome contradictions and limitations, a way of interaction of complex systems is an inevitable, normal phenomenon. Of course, conflict involves struggle, but, above all, conflict involves interaction. It is shown that the conflict can’t be considered as an optimization task, since with equal resources of the parties, the conflict will be terminated due to the complete depletion of both sides, and with unequal resources, the defeat of the weaker side with a probability of one. Also, the conflict can’t be resolved within the framework of the theory of adaptation. A brief comparative analysis of the possibilities of using varieties of Markov processes and the degree of their adequacy to the real processes of supporting offset transactions at different stages is carried out. A mathematical model of the conflict between the parties is proposed. In the model, the process of conflict development is a branched semi-Markov process, the transitional and final probabilities of which depend on the ratio of resources of the parties. In addition, the conflict represents a sequence of concerted actions of the parties and, in fact, is a controllable quasiperiodic process with elements of stochasticity. The resulting winnings of the parties to the conflict are investigated with varieties of their cooperation and rivalry. The proposed model can be used to model the processes of development and implementation of offset programs and the wins of the parties.

Application of Combinatorial Techniques to the Ghanaian Board Game Zaminamina Draft

Games happen to be a part of our contemporary culture and way of life. Often mathematical models of conflict and cooperation between intelligent rational decision-makers are studied in these games. Example is the African board game ’Zaminamina draft’ which is often guided by combinatorial strategies and techniques for winning. In this paper we deduce an intelligent mathematical technique for playing a winning game. Two different starting strategies were formulated; center starting and edge or vertex starting. The results were distorted into a 3x3 matrix and elementary row operations were performed to establish all possible wins. MatLab was used to distort the matrix to determine the diagonal wins. A program was written using python in artificial intelligence (AI) to help in playing optimally

A dynamic spatial model of conflict escalation

In both historical and modern conflicts, space plays a critical role in how interactions occur over time. Despite its importance, the spatial distribution of adversaries has often been neglected in mathematical models of conflict. In this paper, we propose an entropy-maximising spatial interaction method for disaggregating the impact of space, employing a general notion of ‘threat’ between two adversaries. This approach addresses a number of limitations that are associated with partial differential equation approaches to spatial disaggregation. We use this method to spatially disaggregate the Richardson model of conflict escalation, and then explore the resulting model with both analytical and numerical treatments. A bifurcation is identified that dramatically influences the resulting spatial distribution of conflict and is shown to persist under a range of model specifications. Implications of this finding for real-world conflicts are discussed.

Ransom Demands by Pirates: Study of the Problem as a Bargaining Game

Game theory has been defined as “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”.1 It finds application in many diverse fields and has bee...

Mathematical model of conflict with non-annihilating multi-opponent

In this paper a conflict composition for non-annihilating multi-opponent for a finite collection of positions is introduced and consider the associated dynamical system. The existence of limiting distribution of the conflict interaction is investigated. By means of conflict interaction how the segregation phenomena emerge in the society is shown.

Game theory: mathematical models of conflict

Game theory: mathematical models of conflict

Game Theory: Mathematical Models of Conflict : A.J. Jones, Ellis Horwood Series: Mathematics and its Applications, Series Editor: Professor G.M. Bell (Ellis Horwood Ltd. Chichester Halsted Press: a division of Wiley, New York - Chichester - Brisbane - Toronto, 1980) 306 pp.

Game Theory: Mathematical Models of Conflict : A.J. Jones, Ellis Horwood Series: Mathematics and its Applications, Series Editor: Professor G.M. Bell (Ellis Horwood Ltd. Chichester Halsted Press: a division of Wiley, New York - Chichester - Brisbane - Toronto, 1980) 306 pp.

Book Reviews

Holzman, Alberi G., Operations Research Support Methodology Marcel Dekker, Inc., New York and Basel, 1979, 646 pp—reviewed by John J. Jarvis Makridakis, S. and Wheelwright, S. C., Studies in Management Sciences: Forecasting, Vol. 12, North-Holland Publishing Co., New York, 1979, 392 pp—reviewed by Vincent A. Mabert Gohagan, John Kenneth. Quantitative Analysis for Public Policy, 1980, McGraw-Hill, Inc., New York, 462 pp and McKenna, Christopher K., Quantitative Methods for Public Decision Making, McGraw-Hill, New York, 1980, 425 pp—reviewed by Joseph S. Martinich Jones, A. J., Game Theory: Mathematical Models of Conflict, Ellis Horwood Limited, Halsted Press/J. Wiley & Sons, N.Y., 1980, 309 pp., $45.00—reviewed by R. Chandrasekaran Kennington, Jeff L. and Helgason, Richard V., Algorithms for Network Programming, John Wiley & Sons, Inc., New York, 1980, 291 pp—reviewed by R. E. Thomas Koopman, B. L., Search and Screening: General Principles with Historical Applications, Pergamon Press, New York, 1980, x + 369 pp., $45 ($19.50 paperback)—reviewed by Lawrence D. Stone Booksiaber, Richard M., Option Pricing and Strategies in investing, Addison Wesley Publishing Company, 1981, 222 pp., $18.95—reviewed by John Kensinger Phillips, Don T. and Garcia-Diaz, Alberto. Fundamentals of Network Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1981, 474 pp—reviewed by Richard V. Helgason and Balakrishna Shetty Rubinstein, Reuven Y., Simulation and the Monte Carlo Method, John Wiley & Sons, New York, New York 07511, 275 pp., $32.95—reviewed by Paul Gray Waison, Hugh J., Computer Simulation in Business, John Wiley & Sons, New York, 1981, 358 pp—Bruce L. Golden

GAME THEORY: MATHEMATICAL MODELS OF CONFLICT (Mathematics and its Applications)

GAME THEORY: MATHEMATICAL MODELS OF CONFLICT (Mathematics and its Applications)

Book Reviews

Abstract Current Issues in Computer Simulation, Edited by Nabil R Adam and Ali Dogramaci Game Theory: Mathematical Models of Conflict, A J Jones

Game theory: mathematical models of conflict, by A. J. Jones. Pp 309. £15. 1980. SBN 0 85312 147 8 (Horwood/Wiley)

Game theory: mathematical models of conflict, by A. J. Jones. Pp 309. £15. 1980. SBN 0 85312 147 8 (Horwood/Wiley)

Three-generation family conflict

Under what circumstances will a vertebrate grandparent be selected to ‘spoil’ its grandchild in defiance of the wishes of the child's parent? To answer this question (the ‘doting grandparent problem’) a mathematical model of conflict and coalition in an animal society, some or all of whose members may possess imperfect information about potential costs and benefits of acts affecting themselves and their kin, is applied to interactions within extended families in diploid, outbreeding species. The model predicts that natural selection will not favour grandparent-grandchild alliances against the parent unless direct costs and benefits of behavioural acts over which conflict may occur are sufficiently broad in impact to affect at least three different kin categories simultaneously.