# Dalton Mabery comments on I’m taking a course on game theory and am faced with this question. What’s the rational decision?

• That’s what I’m wondering too. I don’t think there is a correct answer, but I guess it’s more of a “how did you think about whatever answer you gave?”

• One concept you may be looking for is diminishing marginal utility of money. If I gave you a million dollars, it would give you some amount of happiness. If I then gave you another million dollars, it would again give you some happiness, but less than previously. Because the difference in quality of life between “not a millionaire” and “millionaire” is much greater than between “one-millionaire” and “two-millionaire”.

(Unless you owe exactly 2 million dollars to a crime boss who will kill you tomorrow if you don’t pay him the money. In such case, the second million is the one that makes you more happy. But this is a special case, where certain amount of money gives you something that a part of it couldn’t give you partially. Most situations are not like this.)

As an approximation, it is said that happiness from money is proportional to the logarithm of the amount. But the logarithm does not apply to the extra money you get, but the total money you have. So the information that we lack about the person making \$30K is whether they are living paycheck to paycheck, or they have savings, or possibly an extra source of income.

Generally, “\$30K for sure” is better than “depending on a coinflip, \$60K or nothing”. But how much better it is, that depends on how much money you have otherwise. If literally zero, then the coinflip means that with 50% probability you will starve and die. On the other hand, if you already are a millionaire, then these two options are almost equal. So if you had a choice between “N for sure” and “coinflip: \$60K or nothing”, the millionaire would not accept N smaller than \$30K, but a starving homeless guy might settle for much less.

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Now, a bit more out-of-the-box:

As Dagon already said, this is not a raise. The company is just trying to distract you from the fact that they said no. Update your CV and start looking for a new job.

In the meanwhile, I would probably take the Option B. In theory, the bonus is between zero and infinity, which sounds great… but in practice, a company that refuses to give you a raise will probably be stingy about a bonus, too. (If the bonuses are so secret and unpredictable, they had an option to give you e.g. a \$5K raise and then silently subtract the money from your next bonus; you would never find out.)

• I think this is exactly what I was looking for, but couldn’t put it quite so eloquently. Thank you.

I put Player X on a game show and imagined they had the choice to keep the \$30,000 they have, or risk it for double or nothing. As you mentioned, if that player went on the game show because they had a \$30,000 debt to pay before they lost their house, they’re going to keep the money and pay off that debt.