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A survey of critical structures in competitive games

Department of Mathematics, Semnan University, Semnan, Iran

One of the biggest problems of human society is facing crises. Origins of many crises goback to strategy selection in the relations between human beings. The international community is facedwith many crises, such as poverty and lack of development of a large section of human society, globalwarming, economic crises, the incidence of infectious diseases, the accumulation of weapons of massdestruction, wars, migration, lack of food and clean drinking water are among the crises that threateninternational community. Each of these challenges alone would require measures and facilities that inmany cases are beyond the limited resources of the international community. In this article, the criseshave been discussed, whose origin is relations between human beings. By defining critical points in2 x 2 games, we provide a mathematical model to detect this type of crises, and then by defining aunique compromise point, we offer solutions for this type of crisis. Sometimes the compromise pointcorresponds to the Nash equilibrium, and sometimes better than Nash equilibrium. We believe thatwhat is presented in this article can help fill the void. Fixing the vacuum in game theory and optimaluse of compromise and critical points leads to the development of cooperation–cooperation strategy inthe world.
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