Faster diagnosis prevents apathy in social-distancing epidemic games

Within the epidemic game literature, there is an inconsistency over whether increases in infection risk can discourage prevention practices. In one theory, investments in social distancing and prophylaxis increase monotonely with infection pressure, while in another, there is a turning-point beyond which investments drop off. To-date, the reasons for this difference have been unclear. This article shows that the discrepancies are due to different information assumptions and can be resolved by explicitly modelling diagnosis events. After constructing a unified theory, we find that there is a turning-point in the strength of self-protection as a function of infection pressure. Beyond this turning point, increased risk begins to discourage prevention. Diagnosis rate controls the location of this turning point. The presence of the turning point can be interpreted as a consequence of decision making under incomplete information, where agents must hedge uncertainties in their current state. Without a reasonable chance of diagnosis, individuals are best-off apathetically assuming they are infected and abandoning prevention once infection pressures are sufficiently high. But with reliable diagnosis, prevention remains worthwhile. To conclude our analysis, we estimate turning-point conditions for the specific case of HIV in some African nations, and confirm earlier conclusions that even without diagnosis, increases in risk will always realistically promote prevention and are consistent with perfect-information hypotheses.