Introduction to Game theory

Let’s talk a bit about maths! Don’t worry, it’s nothing too complicated. Actually, we’re going to talk about game theory. Have you ever heard about it? This article will be a brief introduction to this concept.

First, what is game theory?

The game theory is a mathematical concept that studies the most strategic way to win in an interactional game with multiple decision-making players.

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It has many applications in all fields of social science, as well as in logic, systems science, and computer science.

Let’s see one example to illustrate the game theory —

The case of Bonnie and Clyde

Imagine there has been a robbery in a bank recently. We have 2 suspects: Bonnie and Clyde. The police decide to interrogate the two suspects separately.

Each of them has 2 options: to remain silent or to accuse their partner. According to what Bonnie and Clyde will decide to do, here’s what they could risk :

• If Bonnie doesn’t reveal anything and Clyde does the same = they could both get 1 year of prison each.
• If both of them accuse their partner = each of them will get 5 years of prison.
• If one of them accuses his partner and the other one remains silent = the one that was accused will have 10 years of prison and the other one will be set free.

So, logically, the choice that could make less damage for both of them would be to cooperate and remain silent.

This way, each of them would only have 1 year of prison.

But, Clyde could be tempted to accuse Bonnie in order to be set free. So the best move for Bonnie is to do the same, so she wouldn’t end up with 10 years of prison.

But, they would still both lose many years.

So this theory shows the best choice is always to cooperate.

This case scenario is called the prisoner’s dilemma. In a regular game, player 1 and player 2 both have the two same options: to cooperate or to betray. And their total gains will depend on each player’s decision.

It’s important to note that the prisoner’s dilemma doesn’t apply to zero-sum games.

A zero-sum game is a game like chess or poker where the total game sum is constant.

Here we have the example of a chess game where we can see that the sum of wins and losses always equals 1 no matter if the white wins or if it’s a tie.

So if one wins, the opponent loses, so no one has any interest in cooperating.

On the other hand, we can keep the example of Bonnie and Clyde for a non-zero-sum game where we can clearly see that their years of prison in total depends on their decisions, with only two years if they cooperate.

Now, let’s talk see an example illustrating the Game theory in economy.

Game theory in economy

A very simple example of a prisoner’s dilemma in the field of economy is the value of the market price.

Let’s say we have two companies that both sell clothes and each of them controls half the market.

They both have the choice between raising or lowering the price.

• If they both lower their prices, as they are the two only actors in the clothing market, their position in the market will stay the same, they will just both make less benefit.
• If only one of them lowers the price, that company will get all the clients and the other one could be in bankruptcy.
• And if they both increase their prices, their position in the market will still stay the same, and they will make more benefits. So it’s the best choice for both of them, but it won’t be a good thing for the clients.

So it is the reason the authorities regulate market competition and prices.

Well, I think now you get the idea of the Prisoner’s dilemma. Now let’s see how can have a good strategy to win when you face the prisoner’s dilemma.

Strategies to face the prisoner’s dilemma

The mathematicians tried multiple strategies such as the :

• The nice strategy: where we decide to always cooperate. It’s an optimistic strategy where we assume that the other player will also play nice. In this strategy, we will never betray anyone for our personal interest and only if the opponent makes a bad move, then we can betray them.
• The mean strategy: where we always betray. This strategy has been proven to make sure you always get more points overall than the other player. But the overall game sum will not be the best.
• The lunatic strategy: where we betray once every two rounds randomly.

• Unforgiving strategy: where we always cooperate, and once our rival betrays us once, always betray them back until the end of the game.

But these strategies are not the most effective ones.

Anatol Rapoport, a psychologist, and mathematician, has conducted a game tournament in order to study game theory and different strategies to face the prisoner’s dilemma.

The result of that tournament was that the best strategy to win more points overall is :

The Win-Win strategy

The Win-Win strategy is quite simple :

On the first round, cooperate. Then replicate the rival’s previous move for the next rounds until the end of the game.

The Win-Win strategy is a short-term memory strategy, a forgiving strategy.

Can mathematics teach us life lessons on how to behave socially ?

In real life, each time we are facing a situation that reminds us of the Prisoner’s dilemma, unfortunately, the win-win strategy will not be our first instinct because we, as humans, are very selfish, greedy, and we don’t forgive or give our trust easily but mathematics shows, it’s the best attitude to have if we want EVERYONE to win. Otherwise, the mean strategy will be enough to ensure you have more points than your rival, but you won’t have more points overall together.

So maybe we should act the same way in our social interactions? If someone betrays us, letting them know we are not happy about it but trying to forgive them easily as soon as they start to show they are willing to cooperate.