Why Algorithmic Advice Gets Inflated 알고리즘의 조언은 왜 과장되는가

Strategic Responses to Algorithmic Recommendations: Evidence from Hotel Pricing | Management ScienceUsing hotel revenue-management data, this paper shows that even when an algorithm and the human who acts on its advice share the same goal and the data are unbiased, a pure asymmetry in the cost of changing a decision is enough to make algorithmic advice systematically exaggerated.🔗 doi.org/10.1287/mnsc.2022.03740Strategic Responses to Algorithmic Recommendations

Garcia, D., Tolvanen, J., & Wagner, A. K. (2026). Strategic Responses to Algorithmic Recommendations: Evidence from Hotel Pricing. Management Science, 72(1), 609–626.

✔️ Introduction and Summary

As algorithms take on a larger role in decision-making, “human in the loop” has become the standard safeguard: the idea that a final human check can catch an algorithm’s errors. But that safeguard only works if the human actually intervenes.

The record from the U.S. Department of Justice’s antitrust suit against the rental-pricing software RealPage shows how easily that premise can break down. According to DOJ filings, a recommended rent could be accepted for an entire portfolio with a single keystroke, or even set to accept automatically, while deviating from a recommendation required the property manager to justify the decision, and if the company wasn’t satisfied with the justification, the case was escalated to a supervisor. The result: more than 85% of final rents landed within 5% of the recommended price. The legal issue in that case was collusion, a different question from the one this paper takes up, but the two share a common thread: when accepting is easy and deviating is effortful, a human’s decision-making authority can end up merely nominal.

This paper argues that this kind of structure changes the content of the advice itself. If an algorithm knows that the person receiving its advice rarely acts on it, then inflating the advice in advance is, from the algorithm’s own perspective, the rational response. Until now, distortion in algorithmic advice has mainly been explained by bias baked into training data, or by “algorithm aversion,” people’s tendency to distrust and ignore algorithmic advice (Dietvorst et al., 2015). This paper offers a third, distinct explanation. Even with unbiased data and fully aligned goals between the two sides, advice can still be systematically distorted by one thing alone: a difference in how costly it is for each side to change a decision.

✔️ Research Content and Logic

The Conflict of Interest Created by Asymmetric Adjustment Costs

The model economists typically reach for to explain distorted advice is cheap talk: a framework for situations where non-binding messages are exchanged, and where distortion is usually attributed to a divergence in what the two sides prefer (Crawford & Sobel, 1982). This paper’s setup is different. The revenue-management firm that operates the algorithm treats its clients’ revenue gains as a sales asset, so a hotel’s revenue growth is directly in the firm’s own interest. Even with preferences fully aligned, a conflict of interest still arises from a single source: the cost of changing a price. Updating a price costs the algorithm nothing, so whenever the optimal price shifts even slightly, it is in the algorithm’s interest to reflect that change immediately. For the manager, by contrast, updating a price demands time and attention to review the screen and make a judgment call. This cost of the act of changing a price is called the “price-adjustment cost,” and unlike for the algorithm, it is far from trivial for a human. As a result, unless the suggested change is large enough, it is rational for a manager to simply leave the price where it is.

The only lever the algorithm has to close this gap is the number it reports. Reporting a change as larger than it is raises the odds that the manager will act and adjust the price. But this comes at a cost: if the manager takes an inflated recommendation at face value, the price that actually gets set drifts further from optimal, and both the algorithm and the manager share that loss. How much the algorithm chooses to inflate its recommendation, then, is set at the point where two forces balance: inflating more raises the chance the manager updates the price, but it also raises the error that results if the manager copies the recommendation outright. The degree of exaggeration at this equilibrium is what the paper calls the bias factor.

The Manager’s Response and a Two-Stage Cost Structure

Because the manager knows the algorithm inflates its advice, they don’t take the recommended change at face value when entering a price manually. The pass-through rate observed in the data (the share of a recommended price change that carries over into the actual price) is 0.725. The authors caution against reading this number directly as the size of the bias. Cases where the manager enters a price manually, rather than copying the recommendation, tend to occur precisely when the manager’s own read of local conditions points in the opposite direction from the recommendation. If bookings look soft and the manager believes the price should come down while the algorithm is recommending an increase, the manager will ignore the recommendation and lower the price based on their own judgment. As a result, the set of manual-entry cases is systematically loaded with instances where the manager’s information runs counter to the recommendation, which pulls the observed pass-through rate below the true degree of bias. This pattern, where the very sample observed under certain conditions fails to represent the whole, is called negative selection. Left uncorrected, this distortion implies the recommendation is inflated by a factor of 1.39; once the model described below corrects for it, the estimate comes down to the roughly 1.2 mentioned earlier.

There is one feature of manager behavior that a conventional advice model like cheap talk cannot explain. In models like cheap talk, the more extreme the advice (the larger the suggested change), the less likely the recipient is to act on it, since an unusually large ask naturally reads as less credible. The hotel data analyzed in this paper shows the opposite pattern: the larger the swing in the recommendation, the more likely the manager is to copy it outright. The authors explain this with a two-stage cost structure.

Stage	Manager’s Choice	Cost	Outcome
Stage 0	Do not engage	None	Keep the existing price
Stage 1	Give the price screen attention	Attention cost	Access readily available local information
Stage 2	Work out the optimal price directly	Thinking cost	Gather additional information and set the price freely

A large swing signals that the matter is important, so the manager only pays attention in cases like that. But paying attention doesn’t mean the manager can work out the optimal price on their own; that requires a separate thinking cost. This is why most managers stop at Stage 1 and accept the recommendation. The actual price-setting interface matches this cost structure: accepting a recommendation takes a single click, while entering a price manually means switching to a different screen and filling in the values one at a time.

✔️ Data and Methodology

The data came from an anonymous, Europe-based revenue-management service provider. Records from nine of the firm’s hotel clients were used in the analysis: eight resort properties and one urban property. Each hotel was observed for roughly 14 months, yielding about 6 million daily price records and roughly 60,000 bookings. The unit of observation is a room type paired with an arrival date, meaning a specific product such as a given room sold for a given date.

The hotels in the sample have around 50 rooms each and are family-run operations where managers wear multiple hats, with no staff dedicated solely to pricing. This background likely contributes to the large adjustment costs observed in the paper, and results could differ at a large chain with a dedicated pricing team.

One restriction was applied to the sample. The main sample used in the analysis is limited to observations where the prior price matched the recommended price (N = 2,017,932, about 34% of the total). Restricting the sample this way allows any gap between the recommendation and the actual price to be interpreted as arising from information processing at that specific point in time. It also rules out a feedback effect, where a manager’s past manual entries loop back to shape the algorithm’s future recommendations. Price changes were measured as ratios by converting each day’s price to a log value and comparing it to the prior day; a price update was defined as any day this value changed.

Four Facts Observed in the Data

Before presenting the model, the paper first lays out the following regularities found in the data.

Managers update prices far less often than the algorithm updates its recommendations. The algorithm changes its recommendation on average every 7 days, while the manager changes the actual price on average once every 35 days. The larger the swing in the recommendation, the more likely the manager is to actually update the price: the update probability is just 0.6% when the recommendation doesn’t change at all, but rises to 14.3% when the recommendation shifts by more than 10%. The same logic applies to copying: the larger the swing, the more likely the manager copies the recommendation outright, with the copy rate rising from an overall average of 84.0% to 95.0% when the change exceeds 10%. Conversely, when the manager enters a price manually rather than copying the recommendation, the change in the recommendation isn’t fully reflected in the actual price: the pass-through rate is only 72.5%, and stays around 73% even after controlling for other factors.

The relationships between swing size and update probability, and between swing size and copy probability, hold up even when comparing only observations within the same hotel, the same booking horizon, and the same arrival month, meaning they aren’t a coincidental correlation driven by seasonality or hotel-specific characteristics.

Model and Estimation Method

In the paper’s model, the loss a manager incurs is proportional to the gap between the actual price and the optimal price. The optimal price, in turn, is made up of three kinds of information: private information held only by the algorithm, local information the manager can access immediately by paying the attention cost, and information that requires additionally paying the thinking cost to obtain. The manager cannot observe the algorithm’s private information directly and can only infer it indirectly through the recommended price. But as established above, the algorithm doesn’t pass this information along as-is; it inflates it by some fixed factor. The paper’s notion of “equilibrium” refers to the state where the degree to which the algorithm actually inflates its advice exactly matches the degree of exaggeration the manager expects. This equilibrium assumes the manager knows precisely how much to discount the recommendation.

Applying this model to the actual data required estimating several values: the degree of exaggeration, the share each of the three information types contributes to the optimal price, and values capturing how much decision-making costs vary from case to case. These were estimated using the Method of Simulated Moments (SMM), which repeatedly simulates the model on a computer and adjusts these values until the simulated results converge as closely as possible on the values actually observed in the data. Seven moments were used as the basis for comparison: the relationship between price and the dispersion of the recommendation at the time of an update, the rate at which the recommendation is copied outright, the average update rate, and others. The estimation process also imposes the condition that the estimated degree of exaggeration must actually be optimal for the algorithm; repeating the estimation until a value satisfying this condition is found confirms that the observed exaggeration isn’t incidental but a deliberate choice by the algorithm.

✔️ Findings

The Size of the Recommendation Bias

Pooling across all hotels, the estimated bias factor came out to 0.83, meaning the algorithm’s recommendation is inflated by roughly 1.2 times the actual optimal price change, a bias that is statistically distinguishable from zero. Broken down by hotel, this value ranges widely from 0.60 to 0.93, and this spread traces back to how much information the algorithm holds about a given hotel and to how strong the manager’s inertia, or reluctance to change prices, happens to be. The more inert a manager, the more the algorithm tends to inflate its recommendation.

The Distribution of Information

The algorithm’s private information explains only 20–30% of the total variation in the optimal price. The rest is local information only the manager can access, and by value alone, what the manager holds is more than five times larger than what the algorithm holds. The catch is that checking and acting on that information costs the manager attention and thinking effort. As a result, the standard deviation of the actual price ends up smaller than the standard deviation of the gap between the optimal price and the actual price, meaning a large share of the swings in the optimal price never make it into the actual price at all.

The Effect of Delegation

The estimated model is also used to calculate the size of the loss under several counterfactual scenarios. The benchmark is a fully passive manager who never changes the price at all, with that scenario’s loss normalized to 1 and every other scenario’s loss expressed relative to it; smaller values mean a more efficient outcome. Full delegation refers to handing pricing authority entirely to the algorithm, which also eliminates the adjustment cost the manager would otherwise bear.

Scenario	Description	Loss (range across 9 hotels)
Status quo	The current setup, where the manager reviews the recommendation before setting the price. Calculated including the adjustment cost.	0.984 – 0.998
Status quo (excluding adjustment cost)	Same setup, but excluding the adjustment cost the manager incurs from checking the screen and making a judgment call.	0.967 – 0.991
Full delegation	Pricing authority is handed entirely to the algorithm, which sets the exact price with no exaggeration.	0.643 – 0.961
Delegation with bias retained	Pricing authority is handed to the algorithm, but the algorithm keeps inflating its recommendations as before.	0.673 – 0.961
No recommendation	The manager receives no algorithmic recommendation at all and sets prices entirely on their own.	0.996 – 1.000

The status quo improves on full passivity by only 1–3%, and that margin shrinks further once the adjustment cost is factored in. Full delegation, by contrast, cuts the loss by 4–36%. What stands out is how small the gap is between the third and fourth rows of the table: even when the algorithm keeps its exaggeration intact after taking over pricing, the outcome is barely different from full delegation without bias. This suggests the bias itself isn’t the main source of the loss. Breaking down where the gains from delegation actually come from: roughly 80% comes from adjusting prices more frequently, about 10% from removing the bias, and the remaining 10% from eliminating the cost of processing information. The fifth row points in the same direction: the loss under no recommendation being nearly identical to full passivity shows just how rarely managers adjust prices on their own initiative.

✔️ Conclusion

What this research demonstrates is a single chain running through three links. Because changing a decision costs something, people rarely intervene; because the algorithm takes that inertia as a given, it inflates its advice; and because people anticipate that exaggeration, they discount the advice before acting on it. What’s striking is that even though both sides predict each other’s behavior with precision, the price that actually results keeps drifting from optimal. What’s more striking still is that neither side is at fault in this distortion. The goals are aligned, the data carry no bias, and the manager isn’t behaving irrationally. And yet a single asymmetry, the adjustment cost, is enough on its own to produce this distortion, a condition that could recur anywhere an algorithm and a human work together.

One implication worth drawing out is that simply keeping a human in the loop is not, by itself, a safeguard. In this paper, the manager held information worth more than five times what the algorithm held, yet most of it went unused, which suggests that keeping human judgment meaningfully present in a system requires designing not the authority to decide, but the cost of deciding. Along the same lines, the paper confirms that merely having a default option available reshapes the incentives on the advice-giving side. Any environment where sticking with the status quo takes one click while deviating requires extra effort, such as a diagnostic-support system for physicians or a parole risk-assessment tool (Berk, 2017), could give rise to the same conflict of interest. Because this result comes from nine family-run hotels with around 50 rooms each, whether it carries over to a large chain with a dedicated pricing organization will likely depend on the size of the adjustment cost there.

The value of this paper extends well beyond the specific context of hotel pricing. A common assumption in designing systems where algorithms and humans work together has been that simply leaving the final decision with a human is enough to catch the algorithm’s errors. This research puts that assumption directly to the test. That a human holds decision-making authority and that this authority is actually exercised are two entirely different things, and as long as an adjustment cost exists, this paper shows with data that the authority remains nominal while the algorithm effectively makes the decision. Further, this result suggests that asking where a bias in algorithmic advice comes from may matter more than simply establishing that the bias exists. The right response differs depending on whether the distortion traces back to flawed data, to human distrust of the algorithm, or, as this paper identifies, to a gap in how costly it is for each side to change a decision. Showing that advice can be systematically distorted even when the data are flawless and the manager behaves rationally amounts to a warning for any structure that expects a human to serve as the algorithm’s watchdog. Simply occupying the seat where decisions get made guarantees nothing; creating the actual conditions for a person to intervene from that seat is itself part of the design task, and that is the conclusion this paper leaves us with.

📎 References

• Crawford, V. P., & Sobel, J. (1982). Strategic information transmission. Econometrica, 50(6), 1431–1451. doi.org/10.2307/1913390 — the cheap-talk model discussed in the Research Content section, cited as the standard framework this paper’s aligned-preferences setting contrasts with.
• Dietvorst, B. J., Simmons, J. P., & Massey, C. (2015). Algorithm aversion: People erroneously avoid algorithms after seeing them err. Journal of Experimental Psychology: General, 144(1), 114–126. doi.org/10.1037/xge0000033 — source of the “algorithm aversion” concept mentioned in the Introduction.
• Berk, R. (2017). An impact assessment of machine learning risk forecasts on parole board decisions and recidivism. Journal of Experimental Criminology, 13(2), 193–216. doi.org/10.1007/s11292-017-9286-2 — cited in the Conclusion as another domain where the same structure could recur.
• U.S. Department of Justice. (2024, August 23). Justice Department sues RealPage for algorithmic pricing scheme that harms millions of American renters [Press release]. justice.gov — source for the rent-pricing software example in the Introduction, on automatic acceptance and the process for checking compliance with recommendations.
• U.S. Department of Justice, Antitrust Division. (2025, May 14). United States et al. v. RealPage, Inc., et al.: Competitive impact statement. Federal Register, 90(92), 20505. govinfo.gov — same case, source for the asymmetry between the procedures required to accept versus deviate, and for the finding that over 85% of final rents landed within 5% of the recommended price.