Dynamic, information-asymmetric, and empirically calibrated extensions of the near-miss reporting game: when does reporting reduce future accident risk?

Near-miss reporting systems are a cornerstone of safety management in high-hazard organizations, yet Winkler, Perlman and Westreich (2019) showed with a manager-employee game-theoretic model that whether reporting a near-miss event actually reduces the likelihood of a future accident depends on an unknown reporting-effect parameter, so reporting can fail to improve safety or even worsen it. Their analysis was confined to a single near-miss event, complete information, and one functional form, and that scope leaves three linked extensions open: a dynamic/evolutionary model in which the outcome of one near-miss updates the parameters governing later events so that the accumulation of safety learning over time can be studied; models with asymmetric information between manager and employees; and empirical determination of the reporting-accident parameter beyond a single case study. Later work has built parts of this program — a multi-event repeated game of near-miss handling (Westreich et al. 2021), Bayesian and evolutionary versions of a hospital reporting game (Caspi et al. 2023), tripartite evolutionary games of reporting management in coal mines (Tian et al. 2026), and a prospective cohort study linking company response to near-misses with subsequent accidents (Inagaki et al. 2024) — but no work found to date analyzes the coupled model in which near-miss outcomes feed back into the accident-risk parameters under asymmetric information, and the reporting-effect parameter remains empirically unidentified. The open problem is to close this gap: characterize the conditions under which accumulated near-miss reporting reduces the likelihood of a future accident in a dynamic, asymmetric-information reporting game, and identify the reporting-accident effect empirically.

Background

A near-miss event is an unplanned incident that could have caused harm but did not — a precursor that signals weaknesses in an organization's safety barriers. Near-miss management systems, in which employees report precursor events and the organization analyzes and corrects the underlying risk factors, have been a pillar of safety management in the chemical process industry since the framework of Phimister et al. (2003) and are now standard in construction, mining, healthcare, and transportation. Two difficulties recur. First, employees systematically underreport near-misses, because reporting costs effort, may invite blame, and rarely brings individual benefit, so managers must design incentives for reporting. Second, the assumed safety benefit of reporting is not guaranteed: behavioral studies of near-miss bias (Tinsley, Dillon and Cronin, 2012) show that experiencing a near miss without a bad outcome can create a false sense of immunity and amplify risk-taking, so the net effect of reporting (and of handling the reports) on subsequent accident likelihood is an empirical quantity, not an axiom.

Winkler, Perlman and Westreich (2019) gave this tension a quantitative game-theoretic form. A manager and an employee interact over a single near-miss event: the manager chooses a penalty/incentive level $I$ to motivate reporting, and the employee chooses a resource level $B$ to invest in reporting. The probability that the event is reported is $p(I,B)=\frac{IB}{IB+1}\cdot\frac{E}{E+k}$, where $E$ is the expected cost of a potential future accident per employee and $k$ is a cost coefficient. Reporting then modifies the likelihood of a future accident through a near-miss factor $q(I,B)=Q-\theta p(I,B)$, where $Q$ is a baseline factor and $\theta\ge 0$ is the reporting-effect parameter: $q<1$ means the odds of a future accident are reduced, $q>1$ means they are increased. A Nash equilibrium — a strategy pair from which neither player benefits by unilaterally deviating — exists under stated conditions, and the paper's sensitivity analysis (calibrated with a case study of an Israeli firm) shows that the equilibrium near-miss factor $q(I^*,B^*)$ can lie above or below 1 depending on parameter values: for low $\theta$, equilibrium reporting may fail to reduce the likelihood of a future accident at all, whereas for sufficiently large $\theta$ and expected accident cost $E$ it can reduce the odds. The authors stress that $\theta$, the empirical parameter governing the effect of reporting on subsequent accidents, is uncertain, so the safety benefit of a reporting system cannot be presumed.

The model is deliberately minimal: a single near-miss event, a simultaneous-move game, complete information (manager and employee know all payoffs and parameters), and one functional form for reporting probability and accident-risk modification. Three directions for future work follow from these limitations: (i) an evolutionary or dynamic model in which the outcome of one near-miss event affects the parameters governing later events, so that the accumulation of safety learning over a sequence of near-misses can be studied (an evolutionary game tracks how strategies spread in a population of boundedly rational players according to their relative payoffs, rather than assuming one-shot fully rational optimization); (ii) models with asymmetric information, where for example the manager knows accident costs but employees hold different beliefs about penalties, resource loss, or other reporting considerations (a Bayesian game models such settings: players have private information — their type — and best-respond to beliefs about the other players' types); and (iii) empirical determination of the reporting-accident parameter, testing robustness beyond the chosen parameterization and case study. These three directions jointly serve one objective: establishing when a near-miss reporting system actually reduces the likelihood of a future accident.

Problem Statement

Complete the research program on the strategic reporting of near-miss safety events opened by the manager-employee reporting model of Winkler, Perlman and Westreich (2019, Safety Science 117:365–374, DOI 10.1016/j.ssci.2019.04.029). The common objective is to determine, with a model faithful to the organizational reporting setting and empirically grounded, when a near-miss reporting system genuinely reduces the likelihood of a future accident rather than merely generating reports. The program comprises three linked targets, treated together:

(1) Dynamic extension. Construct and analyze a game-theoretic model of a sequence of near-miss events in which the outcome of each event — whether and how it was reported and handled, and whether a subsequent accident occurred — updates the parameters governing later events, including the reporting-effect parameter $\theta$ and hence, through $q(I,B)=Q-\theta p(I,B)$, the near-miss factor $q$ of the source model, so that the accumulation (or erosion) of safety learning over time can be characterized. The updating law is part of the model to be constructed: the model must state which quantities of the source model ($\theta$, $Q$, $E$, $k$) are treated as state variables and how each near-miss outcome changes them, and that law must be justified from the organizational reporting setting and the available evidence rather than chosen so that the requested conclusion holds by construction. Derive the equilibrium or evolutionary dynamics — either an equilibrium of the sequence game under the stated updating law or an explicit evolutionary dynamic — and give explicit parameter-conditional conclusions stating when equilibrium reporting behavior reduces, fails to reduce, or increases the likelihood of a future accident over time.

(2) Asymmetric information. Extend the analysis to settings in which the manager and employees do not share the same information, and determine how the conclusions of the complete-information dynamic model of target (1) change. This extension must be built on that dynamic model: asymmetric information is layered onto the same near-miss sequence whose outcomes feed back into the accident-risk parameters, so that the target is a single coupled dynamic, asymmetric-information model rather than a separate extension of the source single-event, complete-information model.

(3) Empirical grounding. Determine the sign and magnitude of the effect of near-miss reporting and of the handling of reports on subsequent accident likelihood — the empirical determination of the reporting-effect parameter $\theta$ — from the quantitative empirical estimates reported in the cited literature, and test the robustness of the model's conclusions beyond the single case-study parameterization.

Partial adjacent results exist — repeated games of near-miss handling under complete information (Westreich et al. 2021), Bayesian and evolutionary versions of a hospital reporting game (Caspi et al. 2023), tripartite evolutionary reporting-management games (Tian et al. 2026; Qin and Wu 2021), and one prospective cohort study of company response adequacy (Inagaki et al. 2024) — but none couples near-miss outcomes to the accident-risk parameters of a reporting game under asymmetric information, and the reporting-effect parameter remains empirically unidentified.

References

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