When transparency is a bargain—and when team incentives make it costly

An employer can promise workers a share of a successful project. But if the employer also knows something workers do not—about task difficulty, for example—the information disclosed can change how much compensation induces effort. Transparency and pay are therefore connected design choices, not separate management decisions.

In Transparency in Team Contracts, Paul Dütting, Yingkai Li, Inbal Talgam-Cohen and Jinzhao Wu establish a sharp theoretical distinction. When workers’ efforts are substitutes, full disclosure retains at least 75% of the employer’s best achievable expected payoff. When efforts are complementary, no comparable universal guarantee exists. The paper is an arXiv preprint submitted on November 5, 2026; the supplied record does not establish peer-reviewed publication.

The contracting problem

The authors study a mathematical model, not workplace data or an experiment. A principal delegates a project to several agents. Each agent chooses whether to incur a known effort cost; effort itself is hidden. The project either succeeds or fails, with the principal’s reward normalized to one for success and zero for failure. Success probabilities depend on both the workers exerting effort and an uncertain state drawn from a known, finite distribution.

The principal observes that state. Before it is drawn, however, the principal publicly commits to both a disclosure rule and a payment rule. Every worker receives the same public signal, updates beliefs using Bayes’ rule and knows everyone’s promised payment. Compensation is paid only on success and can depend on the signal, not directly on an undisclosed state.

Workers choose effort in a Nash equilibrium: nobody gains by changing their own choice alone. The analysis selects the equilibrium most favorable to the principal when several exist. Its objective is the principal’s expected reward after payments—not workers’ earnings, output alone or total social welfare.

Why substitutes limit the cost

The positive result requires the success-probability function to be monotone and submodular in every state. Monotonicity means additional effort cannot reduce success. Submodularity means a worker’s extra contribution weakens as more colleagues exert effort: efforts are substitutes in this precise, diminishing-returns sense.

With optimally chosen contracts after each state is fully revealed, the principal receives at least three-quarters of the payoff attainable through any joint choice of public disclosure and contracts. This is the meaning of the paper’s 4/3 approximation factor. It is a worst-case bound, not a prediction that transparency normally cuts profits by 25%. The bound is tight: constructed examples approach it as the number of workers grows, even with additive contributions.

The proof first shows that bounding disclosure’s disadvantage against complete silence, across all relevant settings, also bounds its disadvantage against optimal partial disclosure. It then starts from the team induced under silence and considers which workers to keep incentivizing after disclosure.

A worker whose contribution is low in the revealed state may require an expensive success share. Dropping that worker sacrifices some output but, under submodularity, cannot weaken the remaining workers’ marginal contributions. A mathematical potential function guides these retain-or-drop decisions and establishes the guarantee. The freedom to change which workers are incentivized is crucial; simply keeping the same team need not work.

When complementarity reverses the result

With supermodular production, workers’ marginal contributions increase when colleagues work. Dropping one person can then undermine the team’s effectiveness rather than make others cheaper to motivate.

The authors construct two workers and two equally likely states in which full disclosure leaves the principal zero payoff, whereas withholding all state information permits a strictly positive payoff. Pooling the states changes expected marginal contributions enough to make joint effort affordable. This is an existence result demonstrating an unbounded worst-case relative loss—not evidence that secrecy generally improves complementary teams or makes workers better off.

The paper also provides a computational result for substitutes. A deterministic algorithm combines greedy team selection, pruning and enumeration of workers with large payment requirements. It achieves a 2.311 approximation for known-state contracting, improving on the 6.128 value-oracle factor cited in the paper. Combined with disclosure, it achieves 3.081 for joint information and contract design. These are separate computational guarantees, weaker than the ideal-contract 4/3 bound. Running time is polynomial for fixed accuracy and assumes access to queries returning a team’s production value; practical performance is not demonstrated.

Where the conclusions stop

The results rely on credible advance commitment, shared prior beliefs, public signals and binary effort choices. Allowing mixed-strategy equilibria preserves the transparency bounds, but does not remove favorable equilibrium selection. Private signals remain an open research direction. In a single-worker extension with multiple actions, the worst-case approximation factor instead grows linearly with the number of actions.

These qualifications matter: the paper supplies mathematical guarantees under specified incentive structures, not an empirical verdict on open management. Its central lesson is conditional—transparency’s cost depends on whether a principal can adjust the incentivized team without destroying the value of cooperation.