When better monitoring leaves less money for cooperation

A government trying to encourage cooperation faces more than the bill for rewards. It must also decide who deserves them, tolerate mistakes and pay for the consequences of noncooperation. Those expenses can work against one another: money spent improving identification is money unavailable for incentives.

In a preprint, described in the manuscript as forthcoming in Automatica, Giacomo Vaccario, Luca Verginer and Frank Schweitzer of ETH Zurich investigate that tension using an agent-based mathematical model. Their central finding is conditional but striking: under the assumed costs and decision rules, the best achievable cooperation does not require the most accurate possible monitoring.

A reward scheme that must finance itself

The researchers place agents in repeated prisoner's dilemma interactions with randomly selected partners. In this game, defecting gives an individual a higher payoff than cooperating, whatever the partner does. Yet two cooperating agents together earn more than two defectors. Individual incentives therefore pull against the collective benefit.

An abstract government offers a bonus to shift that calculation. It finances the scheme through a proportional tax on agents' income, including bonuses. There is no accumulation of private wealth in the model: each round generates fresh income and tax revenue.

The authority cannot identify behavior perfectly. With an accuracy above one-half, it correctly rewards a cooperator with that probability, while mistakenly rewarding a defector with the complementary probability. The same accuracy applies to both groups. At one-half, rewards no longer distinguish cooperation from defection.

The budget must cover bonuses and two additional expenses. Identification costs apply across the population and rise with accuracy. Mitigation costs increase with the number of defectors, representing spending needed to compensate for missing cooperation. These are modeled expenses, not estimates from an actual public program.

Why a sufficient bonus keeps changing

The authors derive the minimum bonus that makes cooperation as financially attractive as defection. It depends on identification accuracy, the number of interactions and the current fraction of cooperators. Better identification makes a bonus more effective because cooperators and defectors are less likely to receive the same treatment.

With the payoff values used in the paper's numerical examples, however, the temptation to defect grows as cooperation becomes more common. Maintaining cooperation consequently requires a larger bonus. Success does not automatically make the incentive scheme cheaper.

The researchers also allow agents to make probabilistic choices rather than always select the higher-income option. In this version, sustaining a majority of cooperators requires an additional incentive beyond simply equalizing expected incomes. As the desired stationary cooperation fraction approaches 100 percent, the required bonus grows without bound. Perfect cooperation is therefore unattainable with a finite budget under this decision rule—not a demonstrated limit on real societies.

A comparison scenario lets agents respond to the total income of the cooperating and defecting subpopulations. Some versions support high cooperation with smaller bonuses, showing how strongly the conclusions depend on the assumed basis for decisions.

Chasing a target can backfire

The study combines analytical calculations of stationary states and stability with numerical policy trajectories. A stationary state means the expected cooperation fraction stays constant, even while individuals change strategies.

When mitigation costs are substantial, low cooperation can leave too little money to fund an effective recovery. Different starting conditions can therefore lead to different outcomes. In illustrated cases, adjusting identification accuracy toward a cooperation target also produces recurring rises and falls rather than convergence.

Adding identification costs creates another trap. The chosen cost function makes perfect accuracy infinitely expensive. Pushing accuracy upward eventually consumes funds that would otherwise support bonuses, so cooperation can decline rather than improve.

The authors calculate an optimum by maximizing total payoffs from interactions, excluding bonuses, subject to the stationary-state and budget constraints. With their example payoffs, that means finding the highest affordable stationary cooperation fraction. Simply targeting that fraction can still be unstable: accuracy may overshoot its useful level.

Their alternative policy moves accuracy toward its calculated optimum directly. Illustrated trajectories can then reach the desired state, provided initial cooperation is sufficiently high. The policy is not a guaranteed rescue from every starting point.

A mechanism, not a ready-made prescription

This is a theoretical investigation, not a trial or an empirically calibrated evaluation of a subsidy scheme. Random encounters, symmetric identification errors, specified behavioral rules and an assumed monitoring-cost curve simplify the problem. The later policy-stability conclusions also apply to a continuous-time approximation.

Nor does the analysis resolve privacy, fairness or other ethical questions about monitoring. Its useful contribution is narrower: administrative accuracy and effective incentives compete for the same resources. A policy can become better at identifying cooperation while becoming worse at sustaining it.