We invite you to read one of the most interesting articles written by Maria B. (11 Alfa) for Issue 10 of 𝗠𝗔𝗧𝗛-𝗟𝗬-𝗡𝗘𝗪𝗦, the first Avenor mathematics magazine, initiated by Miss Mihaela Ancuța – Mathematics Teacher, and coordinated by a team of students from middle school and high school.
Have you ever asked yourself why you can always find both McDonald’s and KFC on the same street? Why are there 5 coffee shops around the same corner, but none for the following 5 streets? How is that smart for the businesses? Game theory has the answer.
Game theory is the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants. So put shortly, the way in which people, businesses, governments, and more make decisions when they are interdependent.
Before John Nash developed Game Theory, an economic theory suggested that if everyone did what was best for themselves it would lead to the best possible outcome for society. Game theory refutes this idea and leads to a complete rethink of economics and a Nobel Prize for John Nash. There is actually a fantastic film about this called A Beautiful Mind starring Russel Crowe!
Let’s take the most popular scenario in which this idea comes into play: the Prisoner’s dilemma. Let’s consider two friends, Amy and Trefor, who were suspected of robbing a bank. They were taken for interrogation, into separate rooms and given two choices.
Either they confess and get 2 years in prison, or they deny and only get one year for different offenses in their past. That seems like a no-brainer, obviously both of them will choose to deny.
However, let’s see what happens when their decisions become interdependent. The interrogator adds a new condition: If Amy confesses and snitches on Trefor then she will be given immunity and serve no time in prison, whereas Trefor will serve 3 years if he continues to deny the crime. The same offer is given to Trefor. Considering they do not know what the other will answer, they both confess, avoiding the risk of 3 years in prison.
If Amy assumes Trefor is going to deny the crime, it is better for Amy to confess. If Amy assumes Trefor is going to confess then it is also better for her to confess. Therefore her best choice is always to confess. The same is true of Trefor and both people end up confessing even though it would have been better for them both to deny.
See how their plea changes completely when their decisions become interdependent?. Interesting isn’t it? But how does any of this apply to Economics?
Imagine the following scenario. You sell ice cream on a beach which has no other ice cream shops. Where would you place your cart to attract the most customers? At the center. But one day another ice cream cart appears on the beach. Luckily the owners agree to split the beach in half so both shops are set in the middle of the separated sections.
However, the next day, the competition decides to move right between the two territories, at the center of the beach as that will not only attract the customers on his half of the beach, but also a quarter of the ones on your territory.
The next day, you both set your ice cream carts back-to-back at the center of the beach and realize there is no other place either one can move to gain more customers. This way, neither of you can improve your position without losing customers-this is known as Nash Equilibrium. Nash equilibrium is the position in which nothing is gained if any of the players change their strategy if all other players maintain theirs. The first position of the ice cream carts, although better for the customers, as they had to walk much less, couldn’t last as it did not create a Nash equilibrium.
The same theory will apply to real life. Although many other aspects come into play, marketing strategies, quality of services, price differences and more, at the heart of their strategies, you will always find the principles of Game Theory.