Game Theory

What is Game theory?

Game Theory is the science of strategy. It attempts to determine the actions that “players” should take to secure the best outcomes for themselves in a wide array of “games."

Here, Games don't only include poker or chess. Any interaction between multiple people in which each person's payoffs is affected by other's decision. So If your sister decides to eat the last piece of chocolate cake (you specifically asked her not to) then you won't have any left. You are affected ( left hangry) because of a decision your sister made. This is also considered a game (You might not accept so, but am pretty sure your sister does)

The games all share a common feature, that is, the outcome for each participant depends on the choices (strategies) of all.

These games are generally divided into two

1. Non- Cooperative or Competetive

2. Cooperative

In the first category, the game included a interaction which has winners and losers.

To understand this let's take one famous example

THE PRISONER'S DILLEMA

Nairobi and Rio are two prisoners who were caught for stealing and sent to prison.

Now the police offer them few options.

1. If both of them stay silent and don't snitch on eachother, each have to spend 2 years of prison and then walk out

2. If Nairobi stays silent and Rio snitches, Rio gets to walk free with immunity while Nairobi has to stay in prison for 10 years

3. if both snitch then each have to spend 5 years of prison.

Then they are separated where one doesn't know what the other has done, nor control it.

Above tabular column briefs the options they have

The best option would for both of them to stay shut and get out of prison within 2 years.

But one important thing to consider in this game is that these two prisoners can't trust eachother.

So according to Game theory the best decision to make will be for them both to confess.

Why? Cause this establishes something called Nash Equilibrium.

Equilibrium is obtained when the person makes a decision in which they get the best option whatever the other players choice be.

The player has found nash equilibrium when they make a choice which leaves them better off no matter what their opponents decide.

Here, lets see from Nairobi's pov-

1. If Nairobi decides to confess and Rio doesn't - She gets out with immunity, this compared to the alternate option of not confessing leaves her with 2 years in prison.

2. If Nairobi decides to confess and Rio also confesses- She stays in prison for 5 years, which is half the time she has to spend if she doesn't confess and he does.

That's one example of how game theory is applied. Now in real life they are various other factors to be considered too such as your opponents mental, emotional and phyical tendency.