The Principal Agent Problem

All throughout the world we humans have organized ourselves into a myriad of different social structures and institutions. There are countries, states, and cities, corporations large and small, churches and social clubs, families and friend groups. One thing each of these diverse groups has in common is that they must make decisions. A country must decide whether or not to pass a new law, a corporation must decide where to build their new headquarters, a church must decide how much to pay their pastor and a family must decide what to have for dinner. Each day is filled with so many decisions from so many organizations that if each organization had to come together to collectively decide on a decision each time nothing would ever get done. So how do organizations solve this issue? By appointing agents. An ‘agent’ refers to any person or smaller group of people within a larger organization that is empowered to make decisions on behalf of the larger organizations. Some examples include a parliment passing laws on behalf of a country, a CEO deciding to hire or fire teams of people on behalf of a corporation or a lawyer selling a house on behalf of an estate. It might be tempting to conceptualize agents as leaders or rulers, and while this is frequently the case, an agent needn’t be that grandiose, even small decisions require agents. For example an intern who is given a company card and tasked with going to the store to pick out decorations for an office party would be acting as an agent for the company when they made the decision of what decorations to buy.

Now that we have defined what an agent is we can begin to explore the principal agent problem. The principal agent problem refers to the class of problems that arise for organizations due to the fact that the incentive structure of their agents does not perfectly align with the incentive of the organization as a whole. When what is best for the agent is different from what is best for the organization the agent will of course be tempted to decide in alignment with their own interest which will be to the detriment of the broader organization. Principal agent problems can arise in many forms from blatant corruption to something much more insidious. Lets take a look at a few examples.

The basic variant of the principal agent problem occurs when the incentives of the agent are sufficiently disconnected from the incentives of the organization such that there exist outcomes A and B that the agent is empowered to choose between and whilst A is a better/more desired outcome for the organization as a whole B is a better outcome for the agent. An extreme example of this would be if a minor employee were given unlimited access to company bank accounts to buy whatever they wanted. It should not require much explanation to demonstrate why this could cause problems for the company. Humans always have their own goals and desires and these will never align perfectly with the goals with the goals of a broader organization. So how then, can even this basic version of the principal agent problem be solved? The standard solution consists of 2 parts. Firstly the institution can add incentives to the agent so that outcomes which are better for the institution are better for the agent as well. These incentives can take the form of monetary bonuses/raises, opportunities for advancement and more power in the organization or merely the respect and admiration of their peers within the institution. Secondly, the set of actions that an agent is empowered to choose between is constrained to remove choices where a value conflict might remain. The intern who was given the company card is empowered to choose between buying blue balloons or red streamers but they are not empowered to use the company card to buy themselves a new car.

When these solutions to the basic variant fail we get the problem more commonly known as corruption. This could be nepotism, ie a manager hiring a relative or friend of theirs even though they are not the most qualified candidate or (implicit) bribery, ie a congressmen voting for a law that would help their political donors even though it’s not beneficial to the country as a whole, or even straight up theft, ie an employee who is given access to company funds uses the opportunity to siphon money into his own account. Corruption occurs because either the agent has enough power to bend the rules of the organization so that they are able to serve their own interests or enough discretion to do things they aren’t supposed to and get away with it. Much more could be written about corruption and it is undoubtedly an important problem in many societies but in this essay I want to focus more on other ways principal agents problems can arise.

A more subtle variant of the principal agent problem can occur when agents are empowered to make decisions involving risk or uncertainty. When risk is involved the agent is no longer choosing between outcomes themselves instead they are choosing between probability distributions over outcomes. What this means is that even if there exists a monotonic mapping between the utility of an outcome for the organization and the utility of that outcome for the agent that there can still be instances where the agent will act against the interests of the organization. Lets illustrate this with a toy example and then give a couple instances where it comes up in real life.

Imagine that there are 3 possible outcomes which we can call A, B and C. Outcome A gives the organization 0 units of utility and the agent 1 unit of utility. Outcome B gives the organization 9 units of utility and the agent 2 units of utility. Outcome C gives the organization 10 units of utility and the agent 7 units of utility. Note that for both the agent and the organization the outcomes have the same ordering. C > B > A. This means that if the agent was given a straight choice between any 2 of the outcomes and they choose according to their own interests they will incidentally also choose the best outcome for the organization. This means we won’t run into the principal agent problem with straight choices. But look what happens when we incorporate uncertainty. Suppose the agent has to choose between a course of action that will bring about outcome B with certainty and a course of action that will bring about outcome A with 50% probability and outcome C with 50% probability. The agents expected utility with the first course of action is 2 and with the second course of action is 4 so the agent is incentivized to pick the second course of action however the organizations expected utility is only 5 with the second course of action versus 9 with the first course of action so we have a case of misaligned incentives at the level of choices even though their incentives were aligned at the level of outcomes. In this toy example the agent was incentivized to take the riskier course of action while the less risky course was actually better for the organization but the opposite problem is also possible if we simply change up the numbers a little bit. This problem arises because even though the relationship between utility for the organization and utility for the agent is monotonically increasing it isn’t linear so the monotonicity does not extend to the linear combinations of utilities that we obtain from probabilistic combinations of outcomes.

Now let’s see how this plays out in the real world. First an example where the agent is incentivized to take on too much risk. Lets examine hedge funds. In a hedge fund, investors give their money to a fund manager who then trades with it and attempts to make profits, this is a venture that inherently involves risk and uncertainty because there is no way to be sure about how an investment will turn out before it’s made. The hedge fund manager is thus acting as an agent on behalf of the investors. The common way that hedge fund managers make money is by taking a performance fee, that is a cut, traditionally 20%, of any profits that are earned by investing. Within the spectrum of outcomes where the hedge fund makes a positive profit this creates a linear relationship between the profit for the investors and the profit for the manager, since profit is not necessarily linearly related to utility this unfortunately doesn’t guarantee a linear relationship between the utilities of the two parties but assuming that investors can choose a manager with similar risk tolerance to them it will likely be close. But problems arise when we start to include possible outcomes where the manager loses money. The performance fee can’t go negative so the nice linear relationship we had previously breaks down. The manager still has other incentives to avoid losing money, losses could cause investors to pull their money from his fund and could dissuade potential future investors which would cut into the managers expected future profits and if the manager had some of his own money invested in the fund, which is standard, he would have to eat the losses on that portion. Furthermore, if the manager loses money in a way that can be spun as negligent he can be sued by the investors, though this is rare. Despite all of this the manager is still largely protected from the worst of the losses and this incentive structure is reflected in their investments. The ideal risk structure for a hedge fund manager would be a portfolio of investments that has a high (80-90%) probability of doing well and out performing the market and low but significant chance of blowing up and taking a large loss. This allows the manager to, in all likelihood, have several years of solid outperformance which will attract more and more investors to the fund and then when the inevitable blow up finally does happen the manager can simply close the fund and walk away with the performance fees they had collected during the good years. This is a known problem within the industry but that doesn’t mean it’s a solved one. Investors can try to interview funds and review strategies before investing but the informational asymmetries that exist between the manager and the investor make doing this thoroughly difficult. For this reason hedge funds are broadly considered to be a riskier class of investment and it is considered unwise to invest too high of a percentage of your net worth in any single fund.

The opposite direction can be even more insidious and I believe that it is a large factor in the institutional decay and pervasive inefficiencies that plague our schools, universities and government agencies. Let’s look at the life of a university president. If he messes up and there is a scandal at the university, he gets fired, has his name dragged through the mud in various news articles and on social media and he likely has to start a new career. If he does mediocre and business at the university carries on as usual then he collects his generous but not obscenely high salary, drives his nice car paid for by the university and is generally well respected within his community. If he performs incredibly and saves the university $100 million dollars while also improving the educational experience for the vast majority of students then he collects his generous but not obscenely high salary, drives his nice car paid for by the university, is generally well respected within his community, plus, he gets a really nice article written about him in the alumni newsletter. It should be pretty obvious what the issue is here. The president is heavily incentivized to avoid scandals but only mildly incentivized to improve the university. This means that courses of action that will likely make things better but which have a small but non-trivial probability of scandal will be avoided to the detriment of the university. One way that this plays out is an intense infatuation with referring things to committee. Committees are not always a bad way to decide things, for an important decision getting multiple inputs can be helpful but taken to excess it can slow things down to a glacial pace and contribute to a bloated administrative budget. Committees are a very important tool for an agent whose primary incentive is to avoid scandals. If a decision is made that upsets some people and you are trying to diffuse responsibility so it doesn’t come back to bite you one of the best things you can say is “This decision was made in accordance with all relevant standard procedures and with the unanimous support of the relevant committee”.

We can see that there is a nice duality between the two examples. While in the hedge fund example the principal agent problem arose due to the agent being protected from downside risks causing the utility mapping to become convex and incentivizing excessive risk taking possibly to the point of total ruin. In the example of the university president the agent is especially exposed to downside risk and has a capped upside. This causes the utility mapping to become concave which in turn incentivizes a paralyzing aversion to risk and ensuing stagnancy and bereaucratic bloat. Either of these problems can arise in all different types of organizations, sometimes even both at the same time for different types of risks. Remaining vigilant to look out for cases where these effects may be pushing agents actions in the wrong direction is the first step to fixing this problem and building more efficient institutions.