Would you forgo $10,000 in cash for your best friend to get $100,000?

Let’s be honest, those that are selfish, or seemingly don’t have a true best friend, will clearly choose to take the 10k. Those that are super rich, but have poor friends, might find this as a good opportunity to help someone out and forgo the 10k. Plus there are those people that know their friend would hook them up with some cash, perhaps they could even swindle more than 10k out of their friend and make their choice even more logical.

But what if your friend doesn’t know you were the reason they earned the 100k? The tables now turn don’t they? Most people that come across 100k probably won’t share with a best friend before family, kids’ college, a house, car payments…etc. After all, we’re not talking about the lottery here, it isn’t MILLIONS! Hehehe

Well it turns out we make different decisions with imperfect information. This question can be looked at through an economic concept called a “prisoner’s dilemma”. Traditionally, it is explained using confessions of a prisoner, hence the name. However, today we are going to dive in with something more fun…MONEY!

Of course, we must begin with a table, but don’t worry it is easy to understand. Basically, you can choose to keep the money, or you can choose to cooperate with your friend. Likewise, your friend has the same choices. Clearly, the income is divided based upon the combination of your choices.

Let’s understand the table first:

YOU choose to cooperate (Which is just the right side of the table, image below for clarity): If your friend also cooperates you can decide to go 50/50, 25/75, 80/20…whatever you agree on really, but let’s go with 50/50 today. However, just because we agree to cooperate doesn’t mean they will, thus they could choose to keep it all. In which case they get 100k and you get zilch! Therefore, when we choose to cooperate, we have a higher earning potential, but still risk coming up empty handed based on our friend’s choice.

Right side of table

Us choosing to keep it all (Which is just the left side of the table image below for clarity): Here your friend doesn’t have a choice. You win! You get all 10k. Sure, you could still share it, but then you probably would have chosen to cooperate in the first place. I guess you could argue you don’t trust your friend to cooperate, so you keep it all and still give them money. But honestly, that’s just weird…hahaha. For simplicity sake, you choose to keep it, you get the 10k and they come up empty handed.

Left side of table

Now that we understand the table more clearly, let’s look at what happens with perfect information versus imperfect information:

Perfect information: Looking at the table we can see that the best outcome for all players is where everyone cooperates. That’s the section with the most equal distribution of income. In all other cases we have a situation where someone is better off than the other. Thus, when our friend knows we forwent 10k for them to have 100k, they will likely share their wealth, and everyone’s a winner.

Imperfect information: This becomes a challenge, technically if we cooperate, they could still cooperate and we all win, but will they choose to share with us or someone else? After all, this is when they don’t know you forwent 10k for their benefit. Basically, when they are given the money, they really only know they just won 100k so they are starting out on the “keepin’ it” row. However, we can see that they are better off by not cooperating, so it then becomes a question of self interest.

A true “Prisoners Dilemma”

For fun, look at the table below looking at a confession for a crime. The story goes, you and your friend committed a crime, but no true evidence can prove you both did it to the greatest extent. Meaning, you face a partial conviction at best, and a full conviction at worst. The twist though, is that you are both being detained separately and therefore have IMPERFECT information about the other person’s decision. So what outcome will prevail?

What to recognize here? Notice that both prisoner’s denying the crimes results in the least amount of time in the pen! If one person confesses, they risk 25 years depending on their friend’s choice. However, if both confess, in the pen we all go! Sadly, the system is setup that denying results in the least amount of time being served.

For all you economists you might be wondering why I haven’t mentioned the “Nash Equilibrium” portion of the theory. Let’s save that for next week!

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