Game theory is an interesting field in mathematics revolves around strategic thinking and mathematical models to reach the ultimate decisions. It has applications in all fields of social science, as well as in logic, systems science and computer science you can use as the politicians use it to make smarter decisions in your day to day life but first lets talk about what exactly is game theory, from the book THE JOY OF GAME THEORY by presh talwalkar a functional definition of game theory a game will mean a situation characterized by three components
(1) a set of people involved called players.
(2)a set of allowable moves that each player can make, known as strategies.
(3)a description of how each player feels about the possible outcome.
By now you should know that game theory revolves around strategy and decision making to get the best out come for example in the movie a beautiful mind there was a bar scene "watch it here" game theory was sort of proposed in his thinking if you haven't watched the scene it goes like this there are 5 men and 5 women now one of the women is a blonde girl(suprior) and the other 4 are brunettes you have two choice either go for the blonde or the brunettes in the movie he said the smart outcome is that all men go for the brunettes so that they wouldn't all go for the blonde and get rejected then get rejected by the brunettes for being jerks is this a smart choice though? now lets see our variables as we defined above
(1) 5 men as players
(2) a set of moves can happen the 5 men can either go for blonde or all go for brunettes.
(3) the out come of all going at the blonde vs the out come if they go for the brunettes as it was said in the scene now all of that is called Nash's Equilibrium a very important idea in game theory.
now think if you were in the bar scene what would you do?
Nash's Equilibrium (go for blonde)
let's suppose that all your friend went to the brunettes as you suggested now what is your dominant strategy is going for the blonde as there is no competition. you think that now you have a good shot with the blonde given what other people have chosen that's nash's equilibrium