While browsing through some videos the other day, I came across an interesting experiment. It went as under:

- A group of people were asked to guess a random whole integer between 0 and 100,
- The number chosen was to be closest to 2/3rds of the average of the guesses of all the players
- For example, if the average of the guesses was 66, the correct answer would be 44.

This experiment highlights game theory, which I would like to explore a bit.

Firstly, what is game theory? Game theory is the mathematic modelling of social interactions between people, or simply put, it analyses the behaviour of people in a setting where they are directly competing against each other.

Let’s take the experiment previously mentioned as an example. The thought process to arrive at a guess can be examined in the following manner: the highest possible number that can be chosen/guessed is 100, and the guess corresponding to an average of 100 is 67 (2/3rds of 100). Therefore, 67 becomes the maximum number that one guesses, as 2/3rds of the average of all guesses cannot be more than 67. Keeping that in mind, a logical thinker would then guess 45 to be the answer, as it is 2/3rds of the new maximum, i.e. 67. However, by the same logic used initially, 45 then becomes the new maximum, and it doesn’t make sense to guess any number above it. This cycle keeps repeating until everyone guesses 0. In this situation, the average of the guesses is 0 and therefore the correct answer will also be zero, meaning that in such a situation, all the players win. This situation is known as a Nash Equilibrium. Named after mathematician John F Nash, Nash Equilibrium refers to a situation where every player chooses the strategy that best suits them, considering every other player, and no individual player can gain by deviating from this strategy. For example, in this experiment, the Nash equilibrium is 0, because every player wins if they all choose 0. However, if even one player deviates from this strategy and picks another number, then all the players lose.

So why is game theory important? Game theory influences many business decisions, foreign policy stances and day to day interactions. To quote a simple example to illustrate the application of game theory in the real world, it may be observed that rival businesses, like fast food joints, are usually situated close to each other. To understand this decision, let us take the example of a mobile cart, selling pani puris. Suppose there are 2 people, A and B, selling pani puris in a 1-kilometre radius. A is stationed 0.25 kilometres to the north end, and B is stationed 0.25 kilometres to the south end. There is 0.5 kilometres between the carts, between which the customers can walk to the closest cart. However, in a bid to get more customers, both A and B will inch towards the middle of the stretch of land, i.e. 0.5 kilometres from both ends of the stretch of land. By moving their carts towards the middle, the cart owners retain the original customers on their side of the land, while also getting additional customers from the other side of the land as well. However, since both the cart owners move towards the middle of the land simultaneously, they both end up in the middle of the land, with the same number of customers as before and no way to increase it. Hence, they have reached Nash Equilibrium, as neither of them can improve their position by deviating from their current strategy.

Another application of game theory in business is in a market form called oligopoly. The application of game theories in an oligopoly market form is very interesting and will be discussed in the next blog.

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