Deciding on a reciprocal action with the help of game theory

Document Type : Original Article


1 Researcher, Supreme National Defense University, Tehran, Iran

2 Faculty Member, Supreme National Defense University, Tehran, Iran



A legal but unfriendly act of a country against another country in retaliation for an unfriendly but legal act and in order to force that country to change its unfriendly behavior is called "reciprocal action". The decision of the aggrieved government to choose the type of unilateral action is a challenging one, because its reciprocal action provokes the reaction of the responsible government and the international community. In this article, we model the decision-making situation with the help of zero-sum games. In fact, we correspond the conditions of reciprocal action of the injured government with the game model (X, Y, A) in which X is a set of possible reciprocal actions of the injured government (friend player) against the responsible government, Y is a set of possible reactions of the responsible government (enemy player) and A is the utility matrix of the injured government. We solve the model by Maximin method, in this regard we use the theory of game reduction to a linear programming problem and solve it in MATLAB software.


[1]. بیگدلی، حمید. (1398). مدلسازی مسائل جنگ الکترونیک با استفاده از بازی مجموع صفر، دوفصلنامه بازی جنگ، سال دوم، شماره 5، پاییز و زمستان.
[2]. راعی دهقی، مسعود. (1390). اقدام متقابل و حقوق بین‌الملل، معرفت سال بیستم، شهریور 1390 شماره 6 (پیاپی 165) ویژه ی حقوق،  پژوهشگاه علوم انسانی و مطالعات فرهنگی .
Haywood, O. G. (1954). Military decision and game theory. s.l. : J Oper Res Soc,Vol. 2 .
 Robinson, T. W. (1970). Game Theory and Politics.  Recent Soviet Views. s.l. : Santa monica.
 Berwanger, Dietmar. (2011). Introduction to Strategic Games.
 Rasmusen, Eric. (1989). Games and information: An introduction to Game Theory. s.l. : Oxford, UK: Basil Blackwell.
Thomas, S. F. (2014).  Game Theory. s.l. : 2nd ed, Mathematic Department, UCLA.
 Cantwell, G. (2003). CAN TWO PERSON ZERO SUM GAME THEORY IMPROVE MILITARY DECISION-MAKING COURSE OF ACTION SELECTION?. School of Advanced Military Studies United States Army Command and General Staff College Fort Leavenworth. Kansas Academic Year 02-03.
 Bartlett, P. (2016).  Lecture 7: two player zero-sum games.بITARY DECISION-MAKING COURSE OF                                            د. بعدها ا دیدگاه نظریه‌بازی به بررسی آن‌ها می‌پرداز
 Fox, William P. (2016). Applied Game Theory to Improve Strategic and Tactical Military Decisions,  Journal of Defense Management, DOI: 10.4172/2167-0374.1000147.
 Andreas H, Hamel. & Andreas Lohne. (2018). A set optimization approach to zero-sum matrix games with multi-dimensional payoffs. Mathematical Methods of Operations Research , 88(3).
 Cook, W.D. (1976).  Zero-sum games with multiple goals. Naval Research Logistics Quarterly ,  23(4).
 Ghose, D. & Prasad, U.R. (1989). Solution concepts in two-person multicriteria games.  Journal of Optimization Theory and Applications, 63(2).
 Yang. Y,  Guo. Y, Feng. L. & Di, J. (2011) Solving two-person zero-sum game by Matlab. Applied Mechanics and Materials ,  Vols. 50-51, pp 262-265.