The Money Envelope: How an Opponent’s Choices Reveal Their Position

In game theory, a smart player accounts for the fact that the choices that other players make reveal a lot about their position. This article will show you how this concept works and how you can take advantage of it, by looking at a round of the money envelope game.

 

The setting

Richard and Bob are the final contestants in a game show called “The Money Envelope”. As the winners of tonight’s episode, the host gives each of them one of five possible envelopes. They know the following things:

  • Each envelope contains a check with either 500$, 1000$, 2000$, 4000$, or 8000$ (so that there is only one envelope with 500$, one with 1000$, etc.)
  • One of the contestants is getting an envelope with twice as much money as the other.
  • After each of them sees how much money he got (in private), he can ask the other person to exchange envelopes (without knowing how much money the other person got). If they both agree, the exchange occurs.

 

Money envelope game.

 

The game

Note: this example involves some simple math. You don’t have to follow the specific numbers too closely, what matters is the concept behind it.

In the current game, Richard opened his envelope and found 2000$. Based on the rules, he knows that Bob got either 1000$ or 4000$, with equal probability.

Richard calculates that he should make the exchange, since he stands to gain more that way; on average, he will earn 2500$ dollars after the exchange, compared to the 2000$ that he’s getting now. This is because there’s a 50% chance he will get 1000$, but there’s also a 50% chance that he will get 4000$ (0.5*1000+0.5*4000=2500).

However, Bob is thinking the exact same thing, regardless of whether he found 1000$ or 4000$ in his envelope:

  • If he got 1000$ and he makes the switch, he will get 1250$ on average. (0.5*500+0.5*2000=1250)
  • If he got 4000$ and he makes the switch, he will get 5000$ on average. (0.5*2000+0.5*8000=5000)

Based on this, we would assume that both players would want to make the switch. However, in reality, the contestants both choose to keep their original envelope. How come?

 

Game Theory analysis

The issue here is that if both Richard and Bob are perfectly rational, and both know that the other person is also perfectly rational, an exchange is never going to take place. We can see why by considering the situation step by step, starting from a slightly different angle:

  • Let’s say that Richard opens his envelope and finds 8000$. Since he knows that he already has the envelope with the most money, he won’t agree to an exchange.
  • In this scenario, Bob has to get 4000$ in his envelope (since Richard got the maximal amount). However, Bob doesn’t know whether Richard got 8000$ or 2000$. What he does know is that Richard won’t agree to an exchange if he got 8000$. Instead, the only way Richard will agree to an exchange, is if he got 2000$. Therefore, Bob can conclude that he himself should not agree to an exchange, since he will lose out on money if he does.
  • Based on this, we know that a player who gets 8000$ won’t ever agree to an exchange, but neither will someone who got 4000$.
  • Now, we’re back at the original scenario, where Richard got 2000$. If Bob has 4000$, then he’s not going to agree to an exchange, as we saw above. Therefore, if Bob is interested in an exchange, Richard can conclude that Bob got only 1000$, in which case Richard will be the one that doesn’t agree to an exchange.
  • Furthermore, if Bob has only 1000$, he knows that the only way Richard will agree to an exchange is if he has 500$ (the minimal amount), in which case Bob shouldn’t want an exchange in the first place.

See the idea here? Basically, before making a decision, each player looks at the other player’s behavior. If the other player wants to make an exchange, the original player can conclude that it would benefit that player more than it would benefit them. Eventually, the only person willing to trade is the guy who got the minimal amount, but no one wants to trade with him anyway.

 

A note on the math

This setting is based on the two envelopes problem/the exchange paradoxIn practice, the assumption that each player stands to gain from making the switch may be inherently flawed (which is why it was originally termed ‘the exchange paradox’). There is a large number of papers on the topic, each offering a different explanation for this, and no consensus on the topic has yet been reached.[1,2,3,4]

In general, most formulations of this problem focus on a situation where a single person is given two envelopes, and is allowed to switch between them. However, the current scenario involves two players, engaged in in a zero-sum game (because one contestant’s gain is exactly balanced by the other contestant’s loss).

In practice, it doesn’t matter that the original motivation to exchange may not exist, because the logic behind the players’ decision to keep their envelope, as presented here, still holds. As always, when reading about game-theory models, you should focus on the concept behind it, rather than on the scenario itself.

 

Summary and conclusions

  • In many situations, the decisions that your opponents make can give you insights regarding their position.
  • Use these insights to make better informed and more strategic decisions.

 

The basis for this strategy and example comes from “The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life”. It’s a good read for someone looking to understand basic game theory and how it applies to real-life situations.

I recommend it over the earlier version of the book (“Thinking Strategically”), because that’s what the authors themselves recommend. However, the difference between the two versions isn’t crucial.

 


Make Your Password Manager More Secure by Changing a Simple Setting

If you’re storing all your password in a password manager (as you should), you might be worried about someone gaining access to your files and brute-forcing their way into your password collection.

The best way to avoid this is by using a strong, random password, which will be impossible for a hacker to brute force. However, with the constant advances in computing power and hacking techniques, the bar for how strong your password should be is constantly increasing.

Luckily, there is a way to significantly improve the security of your password manager, without increasing the complexity of your password, and without much effort on your part.

All you have to do is change a single setting: the number of key transformations (also known as ‘password iterations’). Basically, when you input the master password in order to access your database, the software transforms this key multiple times before checking its validity (a process known as ‘key stretching‘). The more transformations, the longer it takes to check if a password is correct, and the longer it will take someone to brute force their way into your database.

KeePass, for example, currently specifies a default value of 6,000 transformations. However, on most modern computers, you could easily change that number to several million transformations without experiencing a noticeable increase in software loading time. This means that if you increase the number of transformation to 6,000,000, a hacker will now take 1,000 times as long to crack your password, while the program will still load almost instantaneously when you input the correct password.

In fact, KeePass lets you set the number of transformation so that it takes the computer exactly 1 second to check the password. On modern computers, these values can often far exceed the 6 million transformations value.

 

The KeePass database setting for changing the number of iterations/transformation the master password goes though.

 

Keep in mind that the loading time will vary for different devices; this will be especially noticeable if you access the password manage on mobile, so make sure you’re not setting the value too high.

Likewise, the optimal value might be different if you use an online service, such as LastPass, which currently recommends not exceeding 10,000 password iterations for client-side encryption (compared to the default 5,000), though they do allow users to go as high as 200,000.

The setting itself is generally easy to find in all platforms. In KeePass you will go to File > Database Settings > Security. In LastPass you go to Account Settings > General > Show Advanced Settings > Password Iterations.

 

LastPass setting for controlling the number of password iterations.

 

One more thing worth noting: while this post focused on password managers, this advice is also applicable in other types of encryption software. VeraCrypt, for example, allows you to set the number of iterations used for encrypting volumes, using their Personal Iterations Multiplier.

 

Summary and Conclusions

  • The master password to your password manager undergoes multiple transformations/iterations before being verified; this number scales linearly with the time required to login.
  • By increasing the number of transformations, you can easily improve the security of your password database.
  • This will lead to a negligible increase in software loading time for you, but will significantly increase the time it takes to brute force the password.
  • When setting the number of transformations, make sure to account for the different processing power of the devices you will use to login (especially if you use mobile).
  • Instructions on how to do this are generally easy to find. If unsure, search for ‘software name + key transformations’ or ‘software name + password iterations.

 


Why You Should Stop Sleeping with Your Phone Next to You (and What to Do if You Decide to Keep It)

Most of us sleep with our phone within reach. In fact, a 2015 report on “Trends in Consumer Mobility” showed that 71% of American adults regularly go to sleep with their phone next to them, meaning that they leave it on their nightstand, on their bed, or in their hands. It’s highly likely that this number has only increased since then, due to the increased prevalence of smartphones in our lives.

This is a problem, because keeping your phone next to you in bed can lead to a variety of sleep, health, and productivity issues. In the following article you will learn why you are better off putting your phone out of reach when you sleep, and what you can do to reduce its negative effects if you decide to leave it there anyway.

 

Literally a picture of a phone laying on a bed.

 

Why sleeping with your phone next to you is a problem

There are a few main reasons why keeping your phone within reach when you’re in bed is bad for you:

  1. You’re more likely to browse your phone, which makes it harder for you to fall asleep, and reduces your sleep quality. The negative impact of electronic-media usage before bedtime is well-document, and occurs due to a multitude of reasons.[1,2,3,4,5Because of this, avoiding using your phone and other electronic devices before you go to sleep is considered to be an important aspect of sleep hygiene, which improves your sleep quality.[6,7]
  2. It increases the temptation to use the phone if you wake up throughout the night. Normally, you would want to just go back to sleep. However, if you have your phone nearby, you now have the temptation to lie awake and browse Facebook (or perform any other pointless activity), until you eventually fall asleep again. This is obviously not good for your sleep.
  3. It makes it more likely that your phone will be the first thing you see in the morning. The same survey from earlier also shows that 35% of American adults check their mobile device as soon as they wake up; this number is likely higher among smartphone users and younger demographics. It’s not inherently a bad thing, but you should consider whether this is what you want for yourself, or of it’s only something you do out of habit. If you find yourself immediately jumping into email/Facebook/whatever as soon as you wake up, think about how this makes you feel in terms of anxiety and pressure, and about how this impacts your productivity, since you’re now starting your day by cramming this stuff into your head.

Because of these issues, it’s better if you keep your phone out of reach when you go to bed. The further it is, the less temptation you will have to look at it before, during, and after you sleep. You can also take into consideration how its placement will affect your morning routine, and put it somewhere where it won’t be one of the first things you look at in the morning.

If the main reason why you need your phone next to you is so that you can use the alarm to wake up, you should definitely consider getting a separate alarm clock instead.

 

What to do if you decide to keep your phone next to you

A lot of you will probably decide to keep using your phone in bed for various reasons, and that’s okay. Below are some simple tips which can help you reduce the issues associated with doing this:

  1. Use an app to filter out blue light from the phone screen. While exposure to light before bedtime is bad in general, exposure to blue light leads to the most issues in terms of sleep quality. By filtering it out, you solve a big part of the problem, without much effort on your part. Read this article to understand why blue light causes problems, and to get some simple recommendations on apps which filter it.
  2. Turn off the sound on your phone. This prevents late-night messages from interrupting your sleep or waking you up. Obviously, you should turn off ‘vibrate’ as well. If you must keep the alarm activated, most phones will allow you to disable general sounds while leaving the alarm sound enabled.
  3. Turn on airplane mode and turn off the WiFi. This can also help reduce the amount of sound coming from your device (with the potential exception of some notifications). More importantly, this removes the temptation to check messages/emails or to look at things online.
  4. Use an app that blocks other apps during set hours. This is especially helpful if you have a specific site/app that you know is problematic (e.g. something that you browse for hours to procrastinate going to sleep).

 

Summary and conclusions

  • Keeping your phone next to you in bed can lead to problems falling asleep and reduce sleep quality.
  • It can also cause anxiety and productivity issues if it’s the first thing that you look at in the morning.
  • If your main reason for keeping your phone within reach while you sleep is using it as an alarm, consider getting a separate alarm clock instead.
  • If you decide to keep your phone next to you, there are some things you can do to reduce its negative effects, such as using apps that filter out blue light, or turning on flight mode.