When research findings are private, simple success bonuses can be optimal

A funder might reasonably want to adjust a researcher’s rewards when promising evidence emerges. Better prospects mean a smaller success bonus could be enough to motivate continued effort. Yet that apparent saving creates a problem: a researcher who privately observes good news may hide it to retain the larger bonus.

In the preprint Contracting for Experimentation with Private Findings, Yale economist Hongcheng Li shows that this concealment problem can eliminate the advantage of making payments depend on reported findings. Within the model, an optimal contract offers success bonuses determined by calendar time alone. This is a mathematical result presented in a preprint, not an empirical test of research funding.

A project with two kinds of news

Li models a funder hiring an agent to work on a project whose fixed quality is initially unknown to both. Each period, the agent privately chooses whether to incur an effort cost. Work can produce a publicly verifiable success, which generates revenue and ends the relationship. Success is possible at either quality level, but more likely when quality is high.

Work can also produce a private finding. In the main model, that finding conclusively reveals high quality, without itself generating revenue, changing the success process or guaranteeing success. Work is worthwhile overall when quality is high but wasteful when it is low. Repeated work without either success or a finding therefore makes an uninformed agent more pessimistic. Skipping work avoids that unfavorable learning.

The funder commits to the contract in advance. Both parties are risk neutral, discount future payoffs at the same rate, and payments to the agent cannot be negative. Li allows a broad range of arrangements, including wages, success bonuses, report payments and severance, with payments potentially varying according to reporting history.

The analysis first identifies the cheapest incentives for a given work schedule, then chooses the schedule that maximizes the funder’s expected payoff. Mathematical bounds establish the minimum compensation compatible with incentives; Li then shows that a simple bonus schedule attains those bounds while deterring the agent’s available deviations.

Why reporting need not change pay

As a benchmark, Li considers findings that are publicly observable and contractible. After favorable evidence arrives, a low success bonus can cover the informed agent’s expected effort cost. Before a finding, higher bonuses are needed to discourage shirking, which preserves optimism and makes later rewards more attractive.

That arrangement breaks down when findings are private. An informed agent can conceal good news and continue working for the higher bonuses. Truthful disclosure must therefore offer at least the payoff available through concealment. Li proves that these restrictions make report-dependent compensation unnecessary: a single posted bonus sequence can deliver the required incentives without asking for reports.

When the optimal contract induces research, the sequence has two stages. During a finite research stage, bonuses exceed the level needed to motivate an informed agent and rise over time, encouraging even an uninformed agent to work. They then drop to a low, constant level. Only an agent who has obtained favorable evidence is willing to continue working at that level, until success. At the low bonus, the informed agent is indifferent between working and shirking; the modeled outcome selects continued work.

The rising research-stage rewards reflect a learning incentive. Discovering high quality early allows the agent to benefit from the remaining generous research-stage bonuses. As that stage approaches its end, fewer opportunities remain to earn those extra returns, so a larger immediate success bonus is needed. This mechanism produces rising bonuses even without discounting.

Information can have incentive costs

The model also shows why better information need not improve both parties’ outcomes. Making favorable findings more likely strictly improves the maximum surplus achievable without incentive frictions whenever that benchmark involves any work. Under contracting constraints, however, silence becomes more discouraging, potentially strengthening the attraction of shirking. The funder may shorten research enough that both parties lose. Likewise, making findings private never improves the funder’s payoff and can hurt the agent if research is curtailed.

These conclusions have important boundaries. The main finding reveals quality conclusively, but research findings may instead be inconclusive. Li shows that a posted sequence remains nearly optimal when findings are nearly conclusive, but does not provide a general solution for inconclusive evidence. In a separate extension assuming no discounting, success itself can be concealed. Rising bonuses then encourage delayed disclosure, and Li identifies nonincreasing posted bonus sequences that are optimal for a fixed research-stage duration.

The paper draws parallels with funding arrangements in which reports guide continuation while payment amounts are specified in advance. Those parallels are motivation, not validation. The result offers a conditional explanation for contractual simplicity—not evidence that funders should universally replace progress-based decisions or research support with success bonuses.