Principal agent theory in agencies and retainers: incentives that actually work

Every time you hand over a budget, you hire an agent

You run a shop. Someone else runs your ads. You want profit. They want a good month and a fee. Mostly those line up. The trouble lives where they do not, and you cannot see most of what they do all day.

Economists have a name for this. Michael Jensen and William Meckling defined an agency relationship in 1976 as a contract under which one person, the principal, engages another, the agent, to perform a service on their behalf, which involves handing over some authority to decide. If both sides look after their own interests, there is good reason to believe the agent will not always act in the principal's best interest.¹ That is not an accusation. It is what happens when two pay packets share one decision.

The fix is not trust alone, and not surveillance. It is the way you pay. In 2016 Oliver Hart and Bengt Holmström received the Nobel memorial prize in economics for their work on how contracts help people with conflicting interests work together.² Here I apply the ideas I actually use to the deals small businesses sign every day: a fee on ad spend, a return on ad spend target, a commission on revenue.

The businesses and numbers below are invented so that I can show every step. Nobody real, no client.

Worked example: Aoife and her agency

Aoife runs Corrib Candles, an online candle shop in Galway at corribcandles.example. She spends €8,000 a month on Google Ads, and a paid media agency in Cork runs the account. I will call it Lee Quay Media.

Aoife is the principal and Lee Quay is the agent. Aoife decides the budget and the fee. Lee Quay decides, every day, which keywords, campaigns and products get the money and how hard to test new ideas. Aoife sees a monthly report, not the 200 small choices behind it.

Of every euro of revenue, Aoife keeps 45c after candles, packaging, delivery and payment fees. That 45% contribution margin runs through every example below.

The three costs of handing over the wheel

Jensen and Meckling split the price of delegation in three. The principal pays to watch the agent (monitoring). The agent pays to prove they can be trusted (bonding). And the agent's decisions still drift from the principal's, and the money lost to that drift is the residual loss.¹

$$AC = M + B + L$$

Here $AC$ is the total agency cost per month, $M$ is what the principal spends on monitoring, $B$ is what the agent spends on bonding, and $L$ is the residual loss, which is uncertain, so I use its expected value: each possible loss weighted by its probability, as set out in Foundations: expected value.

You cannot push all three to zero. Every euro spent on watching is a euro not spent on selling, and some drift remains whatever you do. A good contract finds the lowest total, not the absence of cost.

Worked example: what Lee Quay really costs Aoife

Monitoring. Aoife spends about four hours a month on the report and the account, at €50 an hour of her time, so €200. An independent auditor costs €600 a quarter, another €200 a month. Monitoring: $M = €400$.

Bonding. Lee Quay writes a weekly summary, gives Aoife full read access and accepts one month's notice. The reporting takes about €300 of their staff time a month. Bonding: $B = €300$.

Residual loss. In four months out of 10, Aoife reckons, the agency pushes an extra €2,000 into campaigns returning only €3,000, which leaves €1,350 of contribution, a loss of €650. The expected loss is $0.4 \times €650 = €260$ a month.

In total, $AC = 400 + 300 + 260 = €960$ a month, 12% on top of the €8,000 she spends. That is no scandal, and it is grand as long as you know it is there. It is a number to manage, and the rest of this article is about the biggest lever on it: how the agent is paid.

Why the problem exists at all: hidden effort and noisy results

Two things must both be true for any of this to matter: a conflict of interests, and actions that are hard to observe. Without either, a fixed fee would do.²

In marketing both are always true. The agency has other clients competing for the same hours, and the result also moves with the weather, the season, a competitor's sale and the latest change to the auction.

Economists call this moral hazard: someone protected from the consequences of a choice tends to choose differently.² An agency paid the same whatever happens is protected from a lazy month. An agency paid only on results is exposed to a rainy one.

Worked example: a bad March

Aoife's Google Ads revenue falls from €40,000 in February to €34,000 in March. Maybe the account was neglected while a bigger client launched. Maybe Valentine's Day pulled orders into February. Maybe a competitor ran a half price sale.

Aoife sees one number, €34,000, and three very different stories produce it. One result, several possible levels of effort: that is the whole engine of principal agent theory. Every scheme below tries to make pay depend on effort without seeing the effort.

A fee on spend pays the agency to spend

One of the most common deals I meet in paid media, here and in a good few other markets, is a fee set as a share of ad spend. It is easy to invoice. It also means the agency earns more every time your budget goes up, whether or not the extra spend makes you money.

What decides whether the next euro is worth spending is the marginal return, what that euro brings in, not the average. With a fee on top, each extra euro of spend costs you more than a euro.

$$\text{mROAS}^{*} = \frac{1 + \phi}{m}$$

Here $\text{mROAS}^{*}$ is the break even marginal return on ad spend, meaning the revenue the next euro of spend must bring in before it adds any profit, $\phi$ is the agency fee as a share of spend (0.15 for 15%), and $m$ is your contribution margin as a share of revenue. Below that line, spending more loses you money. The difference between the marginal and the average return is explained in Foundations: marginal versus average.

Worked example: the €4,000 the agency wants to add

Lee Quay charges an invented 15% of spend. They propose raising Aoife's budget from €8,000 to €12,000. Their own data says the first €8,000 brings in €40,000 of revenue, and the extra €4,000 would bring in another €8,000.

Step one, the marginal return. The extra €4,000 brings €8,000, so the marginal return is $8{,}000 / 4{,}000 = 2.0$.

Step two, the break even line. With $\phi = 0.15$ and $m = 0.45$, it is $1.15 / 0.45 = 2.56$. So 2.0 is below the line, and every extra euro loses Aoife money.

Step three, the whole month. At €8,000: contribution $0.45 \times 40{,}000 = €18{,}000$, minus €8,000 of spend, minus a €1,200 fee, leaves €8,800. At €12,000: contribution $0.45 \times 48{,}000 = €21{,}600$, minus €12,000, minus a €1,800 fee, leaves €7,800.

Aoife is €1,000 a month worse off, Lee Quay €600 better off, and the report still looks healthy: the average return only falls from 5.0 to 4.0. Nobody has to be dishonest, and the agency may be sound people. The contract simply pays for the wrong thing.

A ROAS target rewards a ratio, not a profit

The usual cure for the spend fee is a target for return on ad spend (ROAS), revenue divided by spend. Google's target ROAS bidding works this way: you state the average revenue you want per euro spent, and the system bids to maximise conversion value at that average. Google also warns that a target set too high may limit the traffic your ads get.³

That warning is the principal agent problem in one sentence. A ratio rises when you cut the weaker spend, and the weaker spend is often still profitable. An agency paid a bonus for a high ROAS will cut it.

$$\text{ROAS} = \frac{\text{revenue}}{\text{ad spend}}$$

Here $\text{ROAS}$ is the return on ad spend, $\text{revenue}$ is the revenue credited to the ads and $\text{ad spend}$ is what you paid the platform in the same period. It is a rate, see Foundations: ratios and rates, and an average, which is its weakness.

Worked example: where Aoife's profit actually peaks

Lee Quay's data splits spend into four blocks of €4,000, bringing in €28,000, €12,000, €8,000 and €6,000 of revenue. Profit after ads is 45% of revenue minus spend:

• At €4,000: revenue €28,000, ROAS 7.0, profit $12{,}600 - 4{,}000 = €8{,}600$.
• At €8,000: revenue €40,000, ROAS 5.0, profit $18{,}000 - 8{,}000 = €10{,}000$.
• At €12,000: revenue €48,000, ROAS 4.0, profit $21{,}600 - 12{,}000 = €9{,}600$.
• At €16,000: revenue €54,000, ROAS 3.4, profit $24{,}300 - 16{,}000 = €8{,}300$.

The horizontal axis is Aoife's monthly ad spend. The vertical axis is what she keeps each month after the cost of goods and the ads, once without an agency fee and once after a 15% fee on spend. The takeaway: her profit peaks at €8,000 of spend, at a ROAS of 5.0. An agency rewarded for a ROAS of 6.0 would cut back to €4,000, a lovely 7.0, and Aoife would earn €1,400 a month less. A spend fee pushes spend up, a ROAS target pulls it down, and neither knows where the peak is.

The marginal rule finds the peak. Without a fee, spend while the next block returns more than $1/m = 1/0.45 = 2.22$. The second block returns 3.0, keep it. The third returns 2.0, stop. The auction side of this is in auction theory and bidding strategy.

Rewarding A while hoping for B

In 1975 the management scholar Steven Kerr wrote an article whose title became a proverb: "On the folly of rewarding A, while hoping for B". People work out what is actually rewarded and do that, often to the near exclusion of everything else, and many organisations reward the very behaviour they hope to discourage. Among the causes he listed were a fascination with simple "objective" measures and an overemphasis on the parts of a job that are easy to see.⁴

Marketing's version hides in the word "attributed". Revenue the ad platform credits to itself is not revenue the ads caused, and the easiest sales to claim are the ones that were coming anyway.

Worked example: the brand search shuffle

Aoife agrees a 10% commission on revenue attributed to Google Ads. Lee Quay moves €1,000 a month into ads on searches for "corrib candles", people typing her own name. Those ads are credited with €10,000 of revenue, a ROAS of 10. On paper it is the best campaign in the account.

Then Aoife runs a test. For four weeks she switches the brand ads off in half the country. Orders from people searching her name barely change, because 80% of them find her through the ordinary results anyway. Only 20% of the €10,000, which is €2,000, is revenue the ads caused.

The €2,000 leaves Aoife $0.45 \times 2{,}000 = €900$ of contribution. Against it she pays €1,000 of ad spend and a commission of $0.10 \times 10{,}000 = €1{,}000$. Her result: $900 - 1{,}000 - 1{,}000 = -€1{,}100$ a month.

Lee Quay earned €1,000 for moving credit from one column to another. Aoife hoped for B, new sales. The contract rewarded A, credited sales. Telling them apart has its own toolkit, from holdout tests to causal inference with propensity scores and instruments and media mix modelling.

Pay on what tells you about effort, and filter out luck

Holmström's 1979 paper, and independently Steven Shavell in the same year, gave the first sharp rule for choosing what to pay on.⁵ It became known as the informativeness principle: pay should depend on every measure that carries information about what the agent actually did. A measure that tells you nothing about the effort or the noise is useless, while a measure that moves with the noise in the result, such as a rival's performance or the state of the market, is valuable precisely because it lets you strip that noise out.⁶

The Nobel committee's example is a chief executive paid on the share price, which also moves with the whole economy, so the pay rewards good luck and punishes bad luck. Paying on the share price relative to similar firms is better.² Many real executive contracts fail this test and are, in effect, paid for luck.⁶

In marketing, the market measure is anything that moves with demand but not with the agency's effort: search volume for your category, or a holdout region where the agency changes nothing. The contract becomes a base fee plus a share of the result above an adjusted baseline.

$$t = f + k\,(\beta - \hat{\beta})$$

Here $t$ is what the agent is paid for the period, $f$ is the fixed fee, $k$ is the share of each extra euro of measured result that goes to the agent, $\beta$ is the measured result (here, contribution after ad spend), and $\hat{\beta}$ is the baseline you would expect without any special effort, typically last year's figure multiplied by a market index. Indexing a figure to the market is explained in Foundations: indexing and base rates.

Worked example: a rising market and a falling one

Aoife offers Lee Quay $k = 0.15$, 15% of her contribution after ad spend above a baseline. Last March that contribution was €10,000.

This March, search volume for scented candles, her market index, is 20% higher than a year ago. Her contribution is €13,000.

Without indexing, the share is $0.15 \times (13{,}000 - 10{,}000) = €450$. With indexing, the baseline is $10{,}000 \times 1.2 = €12{,}000$, and the share is $0.15 \times (13{,}000 - 12{,}000) = €150$. The other €300 would have paid the agency for the weather.

Now a month where the market falls 20% and her contribution is €9,000. Unindexed, the agency earns nothing, because €9,000 is below €10,000. Indexed, the baseline is $10{,}000 \times 0.8 = €8{,}000$, and the agency earns $0.15 \times 1{,}000 = €150$ for beating a falling market. The month they worked hardest is the month a naive contract pays nothing.

The noisier the measure, the smaller the share should be

How big should $k$ be? A large share gives strong incentives, but it also hands the agent risk, because the measure is noisy, and people who carry risk want paying for it. This is the classic trade off between incentives and risk sharing.⁶

In the model behind the Nobel citation, a risk averse agent values a contract at the expected pay, minus the cost of the effort, minus a penalty for the variance of the pay.⁶

$$U_A = E(t) - c(a) - \tfrac{1}{2}\, r \operatorname{Var}(t)$$

Here $U_A$ is what the contract is worth to the agent as a sure sum, $E(t)$ is the expected payment, $c(a)$ is the cost to the agent of putting in effort $a$, $r$ is the agent's risk aversion, and $\operatorname{Var}(t)$ is the variance of the payment, the square of its standard deviation, see Foundations: spread. The sure sum is what I called the certainty equivalent in decision theory for founders.

Holmström and Paul Milgrom showed in 1987 that when an agent works over a long period before being measured, the best contract, under some technical assumptions, is exactly linear in the result, which is why the simple $f + k\beta$ form keeps turning up in real deals.⁶ In that linear model, if each unit of effort raises the expected result by a fixed amount, the best share has a closed form.⁶

$$k^{*} = \frac{1}{1 + r\, c''(a)\, \operatorname{Var}(\varepsilon) / \zeta^{2}}$$

Here $k^{*}$ is the best share of the measured result to give the agent, $r$ is the agent's risk aversion, $c''(a)$ is how quickly the cost of extra effort rises (the second derivative of the cost of effort), $\operatorname{Var}(\varepsilon)$ is the variance of the noise in the measure, the part of the result the agent does not control, and $\zeta$ is the agent's productivity, how much each unit of effort adds to the expected result. The variance is explained in Foundations: spread.

Read the formula for its direction. The share is always between zero and one. It rises when the agent is more productive, and falls when the measure is noisier or the agent more risk averse. With no noise, the agent keeps the whole result, like a franchise owner. With overwhelming noise, the agent is on a flat salary.⁶

Worked example: how much share a noisy month can bear

Assume, purely for illustration, that each extra hour of Lee Quay's attention adds €60 of expected monthly contribution, so $\zeta = 60$. The cost of their effort rises by 60c per hour for each extra hour, so $c''(a) = 0.6$. Their risk aversion is $r = 0.0001$. That looks tiny, but variances are measured in euro squared and run into millions, so it bites. The open question is the noise in Aoife's monthly contribution, measured as its standard deviation.

Take a standard deviation of €3,000. The variance is $3{,}000^2 = 9{,}000{,}000$. The noise term is $0.0001 \times 0.6 \times 9{,}000{,}000 / 60^2 = 540 / 3{,}600 = 0.15$, so the best share is $1 / 1.15 = 0.87$.

Double the noise to €6,000 and the variance quadruples to 36,000,000. The noise term becomes 0.6, and the best share falls to $1/1.6 = 0.63$. At €12,000 the term is 2.4 and the share falls to $1/3.4 = 0.29$.

The horizontal axis is how much Aoife's monthly result jumps around for reasons the agency does not control, as a standard deviation in euro. The vertical axis is the best share of the measured result to hand over. The levels are high because this toy agency is the only thing driving the result. Real shares are far smaller. The takeaway is the shape: the noisier the measure, the weaker the incentive, and the curve falls fast. It is also why indexing pays twice: filtering out the market shrinks the noise, and less noise justifies a stronger share.

When one important task is hard to measure, mute every incentive

Real agencies do several things that compete for the same hours. Holmström and Milgrom's multitask paper of 1991 starts there. Its headline result is that the case for paying on any one task falls the harder it is to measure performance on the other tasks competing for the agent's time and attention, and that a fixed wage can be the best contract even when good, objective measures exist for some of the work.⁷

The Nobel committee quotes a line from later work: "Business history is littered with firms that got what they paid for."⁶ Its example is the teacher paid on test scores who teaches to the test and neglects the curiosity nobody can score.²

In an ad account the easy task is harvesting: retargeting past visitors, tightening bids, chasing this month's attributed revenue. The hard task is building: new customers, new creative, better tracking, ground that pays off in six months. Pay hard on the first and the second quietly stops.

Worked example: where 60 hours go

Lee Quay gives Aoife 60 hours a month. Under a 10% commission on attributed revenue they spend 50 hours harvesting and 10 building. Under a base fee with a small quarterly share of indexed contribution, 35 and 25.

The harvesting split wins this month. Its extra 15 hours bring in €2,000 more revenue, all of which I generously count as caused by the ads. That is $0.45 \times 2{,}000 = €900$ of contribution.

The building split wins later. With 25 hours of building the account brings in 75 new customers a month, with 10 hours only 30. Each new customer is worth about €80 of contribution over their first year, a lifetime value figure of the kind explained in Foundations: lifetime value. So the strong commission costs $45 \times €80 = €3{,}600$ of future contribution for every month it runs.

Net, the sharp looking commission costs Aoife about $3{,}600 - 900 = €2{,}700$ a month, invisible in any report until next year.

Who owns the account matters as much as the fee

Hart's half of the prize is about the contract you cannot write. No agreement lists every future situation, so it must say who decides when the unforeseen happens, and whoever holds that right has more bargaining power later. In the committee's words, allocating decision rights becomes an alternative to paying for performance.²

In marketing the decision rights sit in concrete places: the Google Ads account, the analytics property, the conversion tracking, the product feed and the audiences. Whoever owns them can make leaving expensive for the other side.

Worked example: renewal time

Lee Quay set up Aoife's Google Ads account under their own manager account, and the tracking lives in their tag container. At renewal they ask for more.

Leaving would mean a new account without the conversion history, rebuilt tracking and a few weak months. Aoife puts that at €4,000, an invented figure. Lee Quay can now raise next year's fee by up to about €4,000 before leaving becomes the better option for her. No clause in the contract allows it. Ownership does.

Had Aoife owned the account and tracking from the start, with Lee Quay as a user, leaving would cost close to nothing and the renewal would be about results. It is the least expensive fix in this article: one sentence in the contract.

How I put it together

When a founder asks me to look at an agency deal, I run the same sequence. A contract is a game in which the principal moves first and the agent responds, so I solve it backwards: what will the agent do under each clause, then which clauses to pick. Solving backwards is explained in game theory for pricing and positioning.

Worked example: Aoife's new contract

Aoife wants profit and new customers. Building work matters and cannot be scored monthly, so the incentive stays modest. The measure is contribution after ad spend against last year's figure scaled by the category search index, checked each quarter with a holdout region. Extra spend needs a marginal return above 2.22, now that there is no fee on spend. The account and tracking move into her name.

The deal: €1,500 a month base fee, plus 15% of contribution above the indexed baseline, settled quarterly.

In the first quarter her contribution after ads is €36,000. The same quarter last year was €30,000 and the category index is 1.10, so the baseline is $30{,}000 \times 1.10 = €33{,}000$. The holdout region agrees that the gain is real. The share is $0.15 \times (36{,}000 - 33{,}000) = €450$. Lee Quay's quarter: $3 \times 1{,}500 + 450 = €4{,}950$.

The share is small on purpose. The base fee pays for the building work, the share points everyone at the same number, and the index keeps the weather out. My own commission model is a cousin of this one, a base fee or a commission on the added profit, whichever is higher, walked through for a year in commission based pricing month by month.

What incentives cannot do

Contracts are blunt. Kerr made the point himself: some people do the job well with no formal reward at all, and then the one paying them is not causing it, only a fortunate bystander.⁴ A good contract has a modest aim. It should not stand in the way of the right behaviour.

Nor does the theory hand you numbers. The Nobel committee says plainly that it gives no definitive answers, because the best contract depends on the situation. Its power is that it lets you think clearly.² In practice, three questions before you sign. What does this clause pay for? What will a sensible person do to earn it? And is that what I actually want?

Footnotes

1. Michael C. Jensen and William H. Meckling, Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure, Journal of Financial Economics, volume 3, issue 4, pages 305 to 360 (definitions on page 308), 1976, https://doi.org/10.1016/0304-405X%2876%2990026-X

2. The Royal Swedish Academy of Sciences, Contract Theory, popular science background to the Prize in Economic Sciences in Memory of Alfred Nobel 2016, Nobel Prize Outreach, 2016, https://www.nobelprize.org/uploads/2018/06/popular-economicsciences2016.pdf

3. Google, About Target ROAS bidding, Google Ads Help, https://support.google.com/google-ads/answer/6268637

4. Steven Kerr, On the folly of rewarding A, while hoping for B, first published in the Academy of Management Journal, volume 18, issue 4, pages 769 to 783, 1975, https://doi.org/10.2307/255378, cited here from the updated reprint in the Academy of Management Executive, volume 9, issue 1, pages 7 to 14, 1995, https://doi.org/10.5465/ame.1995.9503133466

5. Bengt Holmström, Moral Hazard and Observability, The Bell Journal of Economics, volume 10, issue 1, pages 74 to 91, 1979, https://doi.org/10.2307/3003320

6. The Committee for the Prize in Economic Sciences in Memory of Alfred Nobel, Oliver Hart and Bengt Holmström: Contract Theory, scientific background, The Royal Swedish Academy of Sciences, 10 October 2016, section 2 (the linear contract on page 10), https://www.nobelprize.org/uploads/2018/06/advanced-economicsciences2016.pdf

7. Bengt Holmström and Paul Milgrom, Multitask Principal Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design, Journal of Law, Economics and Organization, volume 7, special issue, pages 24 to 52, 1991, https://doi.org/10.1093/jleo/7.special_issue.24