Game Theory #1

Over the past two months, I’ve been reading up on Game Theory extensively. It has always been a subject of interest for me since undergraduate days. And I’m glad that I found time to read a bit on it. Students that are keen, can also follow the open courseware provided by Yale University for free.

Firstly, this is going to be slightly mathematical (I’m after all trained in Mathematics) and will require some statistics. So let us start by considering the most rudimentary case of Prisoner’s Dilemma, to provide a simple introduction on what follows.

Suppose we have two prisoners and a police officer. Both prisoners are facing a two year sentence. But the police officer offers them a deal now, that if the prisoner cooperate and rat out the other, he will go scot-free while his partner faces seven years of jail. We assume that the police officer offers the same deal to both prisoners independent. So if both chooses to rat, both of them will face five years of jail.

So here, we are facing a situation of strategic interdependence in the sense that each individual’s payoff (jail sentence) depends not only on her own actions, but also on the action of the other individual. As a result, an individual’s best action may depend on what she expects the other player to do. Given this game, what will you do if you’re a prisoner?

Before looking at the game, let us properly define the following:

Dominant Strategy: A strategy that is always the best for a player no matter what other players do.

Dominated Strategy: A strategy that generates worse payoffs than some other strategy for any choices made by other players.

Other words, if you have a dominant strategy here, you should use it while you should use a dominated strategy.

Back to the game, we shall set off a simple playoff matrix here and then analyse the game from there.

So what will I do, I’ll just rat on the other prisoner. Yes, let us be honest and rationale. After all, looking at the table, and assuming he goes through the similar train of thoughts, he probably rat on me. I should do the same to protect my self interests.

Now, any idea why this is called a dilemma? Because each player has a dominant strategy here and the result is Pareto inefficient (socially inefficient outcome).

There isn’t a right or wrong answer here, and it is entirely based on what sort of equilibrium we are looking at. Of course, what kind of people you are dealing with deep down.

I hope this provides a simple introduction to Game Theory. We will look more into various games like auction and business models, as we progress. We will also consider some limitations, like imperfect knowledge. I hope this spark some interest in this subject and gradually show you how Game theory deepens our understanding about a lot of real-world phenomena/ problem!