Research Progress

We finally seem to be making some good progress on our security research project.

The research project that I’m working on with two other students is to find a way to detect perverse incentives automatically. The term “perverse incentive” doesn’t seem to have a rigorous definition, but the idea is that you’re supposed to be acting in someone else’s best interest (whether your employer, your client, society in general, etc.), but it’s in your personal best interest to do something different.

The canonical example of a perverse incentive involves mutual funds. In a mutual fund, you give your money to the mutual fund’s manager, and he invests your money in the market for you. Suppose the fund manager knows there’s a 70% chance the market will crash, and a 30% chance it will boom. The manager can do two things with the money: he can invest it in the market, or he can keep it out of the market (“in cash”). Of course, he can do some combination, putting X dollars in the market and Y dollars in cash. The mutual fund manager’s job performance is measured by how well his investment decisions beat the market average. What does the fund manager do?

The “obvious” answer is that the fund manager keeps most, if not all, of the investor’s money in cash because he expects the market will most likely crash. However, this isn’t what his incentives are, since his job performance is based not on how well the client’s money does, but on the difference between the results of his investment and the results of the market.

There are four possible outcomes:

  • The manager invests the money in the market, and the market booms. The investment’s returns match the market average, so the investor’s job performance is good.
  • The manager invests the money in the market, and the market crashes. The investment’s returns are negative; the client loses money. However, the returns match the market average, since the market as a whole crashed; everyone lost money in the market. The investor keeps his job.
  • The manager keeps the money out of the market, and the market booms. The investment makes no returns. The investor is fired because he underperformed relative to the market.
  • The manager keeps the money out of the market, and the market crashes. The investment makes no returns, but had it been in the market it would’ve done even worse. The investor gets a bonus because he beat the market.

Notice what happens! If he puts the money in the market, he keeps his job either way, since his investments match the market average. But if he doesn’t put his money in the market, there’s a 70% chance he gets a bonus and a 30% chance he gets fired. The chance of getting fired far outweighs the possible bonus. So, he has a perverse incentive to put the client’s money in the market, even though he thinks it will crash; in doing so, he doesn’t risk losing his job.

Today I think our group hit upon the way we need to model this situation. We were trying to use fuzzy cognitive maps, but we couldn’t figure out a way to represent this situation using them. But then we tried just writing out equations for what the expected returns are for an arbitary investment strategy of X dollars in the market and Y dollars in cash. (It’s the same formulas that you learned in grade school for computing compound interest, if you assume, like we are for now, that the market returns at a constant rate.) The market’s rate of return ranges from -1 (you lose everything immediately — total economic collapse) to positive infinity (there’s no limit to how well the market can do).

The mutual fund’s manager job performance is measured by how well he beats the market; in other words, the difference between the return on his set of investments compared to what would’ve happened had he put everything in the market. An interesting thing happens: there’s an upper limit to his performance (if the market completely crashes, he outperforms the market by exactly the size of the client’s money) but there’s no lower limit! This seems important.

Indeed, if you use a little calculus to find how to maximize his job performance, you find that his performance function is a downward-sloping line (assuming you look at his investments’ returns “in the long run” when measured against how much money he keeps in cash. Therefore, the one and only maximum is where he keeps no money in cash, even when he strongly believes the market will crash! The model demonstrates what the expected perverse incentive is.

We haven’t yet played around with the numbers too much to see in what situations this situation will hold. I’d guess that if the investor is 100% sure the market will crash, he’ll keep it out; it’s the threat of the market beating him that keeps him in. Also, limiting the number of periods the market goes through could affect the measure of performance. As they say in economics, “in the long run, we’re all dead.” Practically speaking, there has to be some cut-off point for how long the fund manager’s boss looks at his performance before paying him.

We’ve also assumed that the market performs at a constant rate, and that the investor can’t change his investment strategy during the game. We haven’t yet examined what happens if he can change his strategy while the market’s performance fluctuates. (It doesn’t make sense to let the manager change his strategy while the market remains constant; this allows him to determine with certainty the market’s rate of return and invest accordingly, which eliminates the perverse incentive.)

Of course, the eventual goal is to figure out a way to model perverse incentive situations in general. For example, you’d want to use the model to detect if there’s a perverse incentive keeping a company’s CTO from investing in computer security; the situation there is pretty similar to the one facing the mutual fund manager. Then, once a model is established, you’d want to develop a software tool to evaluate instances of the model to perform that detection for you, instead of running equations manually like we’re doing now.

The success we’ve had today modelling a (somewhat simple) instance of the mutual fund perverse incentive problem gives me some hope that we’re now on the right track for making a good model for this stuff. Looks like that textbook on game theory I read did pay off.

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