Game Theory – Gladiators, Pirates and Games of trust by Haim Shapira

I recently finished reading a book by Haim Shapira – Gladiators, Pirates and Games of trust. I must say that is probably the best introduction that I could have got to the field of game theory.

Game theory is all about interactive decision making – which is what we do in life day in and day out. So, I believe that it makes sense to learn about the topic and get some insights about games people play and learn how to avoid some of the most common mistakes we end up doing and in the process learn about some strategies that we have in our arsenal to use in our day to day life.

Here is a video of Haim sharing delivering a TEDx talk about Game Theory. It’s a short video and even if you are not interested in Games theory, you will still find it funny.

Some interesting games that I have seen play out in real life are as below.

Prisoners Dilema:

This is probably the most famous game coming out of the field of game theory.

Consider the following scenario:

Cops catch two thieves stealing a car. So, they are both sure to get punished for grand theft auto (let’s assume that this results in a 1-year imprisonment for both). However, the cops also believe that they were involved in a murder but can’t prove it.

So, they put them both in different rooms and give them the following offer:

• Confess first and walk free
• If your colleague confesses first, he walks free and you get 15 years prison term

Both of them know that if they both end up confessing, both will end up getting a 10-year prison term.

Now put yourself in the shoes of the thieves and think about what will you do?

• Will you co-operate and not confess (and hope that your colleague doesn’t confess too?)
• Or you confess in the hope that he doesn’t confess, and you can walk free?

In this scenario, if both want to act in their personal interests, both will end up confessing and end up in prison serving a 10-year term. However, if both end up trusting each other and not confess, they can go free after serving just a 1-year term. I guess this is why they have the code – Honor among thieves.

Strangely, this also feels like what siblings face while growing up together.

This is a scenario that plays out many times over in our lives. Consider the situation when you are in charge of growing your business. The times are not conducive and there seems to be a slump. So, you now need to make a decision. Do you want to discount or run a promotion to increase demand?

Unfortunately, you know that your competitor is also facing a similar situation and facing the exact same decision to make, and you can’t talk to each other, as that would be illegal.

So, what would you do? If you discount the price or run a promotion, it could mean that your competitor will do so as well. Now, you have reached an equilibrium again and the impact of the price or promotion was nullified, which is what we see in the market so often.

Reducing price is in neither’s interest. What is needed here is a creative solution that doesn’t involve either of them resorting to discounting. This is not easy to do and is the reason why we don’t see too many people resorting to this option, much to their own losses.

Here are a few other games that people play. It might be worthwhile to explore some of these and at least learn to recognise some of these games when we come across them in our real lives, so that we can go back and learn from the masters about the best strategies and in most cases avoiding the worst strategies.

The Blackmailers Paradox:

Consider the following situation:

You are invited to a room with another person whom you don’t know at all. The person who invited both of you shares that he will give a million dollars to split between both of you. He will walk out of the room and come back in an hour. The thing is if you don’t have an agreement by then, the offer becomes null and void and walks out.

How do you think this will play out?

What if the person you are with decides that he wants to keep 900000 and give you just a 100000.

Will you accept it? What if he says that he is perfectly good to walk out with nothing in hand? Will you believe him and accept his offer or would you rather split the amount equally or not have the money at all? After all, you are still as rich now as you were when you were made this offer. What would you do?

Now consider a variation. In this game, the only thing that changes is that the person making the offer clearly identifies one person who can make the decision (you or your friend). What happens then? This is what game theorists call “The Ultimatum Game”.

What happens if both of you knew that this is going to a game that you will repeat and with roles switched?

You can read more about this here and more of its variants.

Other famous games:

Here are other games to explore Pirates Game, Dead Rich man, The chocolate and poison game, Envelope is greener on the other side (with no known and agreed solution to the paradox), evolutionary game theory, Volunteers Dilemma, dollar auctions, English Auctions, Dutch auctions , first price sealed bid auction, Vickrey auction, Newcomb’s paradox, the chicken game, the fair division problem, traveler’s dilemma.

This is a pretty complex theory and I would strongly recommend reading Haim Shapira’s book – Gladiators, Pirates and Games of Trust in which is he is able make this all simple enough for us to understand the games and also where possible arrive at the best/worst strategies.

One of the things we need to be cognisant of while exploring the world of game theory is that in most cases, the games are explored as if all the players are rational beings who decide based on their own personal benefit maximisation. However, we are all know that we don’t behave in that manner. There is always the cultural, social & moral norms that affect the choices that we make.

Some crucial learnings here are:

1. Playing rationally against an irrational opponent is often irrational.
2. Playing irrationally against an irrational opponent is often rational.
3. The rational way to play most of these games are not really clear.
4. It is hard to impossible to predict how others act in any situation.
5. Incentives are a much better predictor of behavior than anything else.

Also, there is a big difference in the strategies one would employ in a one-time iteration of a game vs a game that will be repeated. In this case, you can learn from the past and improve.

Some crucial learnings here are:

1. Always start by trusting others that they will do what is best for all.
2. Then repeat the behavior you see. IF they trust you, keep trusting them. If they betray you, punish them by betrayal (tit-for-tat).
3. Give people benefit of doubt. Before you start the tit-for-tat strategy, give people benefit of doubt once.
4. Be forgiving. Change your strategy to trust as soon as they start trusting.

In conclusion:

After having read the book, I have come to see some of these games playing out everywhere I see and at every level. I see these games playing out amongst siblings, friends, colleagues at work, between corporates in the marketplace, with customers, partners and even in international politics. I hope to learn enough not to be lured by the worst strategy, while I try and get better at picking the better strategy, given any situation.

PS: Here is a lecture delivered by Prof. Robert Aumann who won a Nobel Prize in Economics based on his work on Game Theory