Testing for COVID‐19 is a key intervention that supports tracking and isolation to prevent further infections. However, diagnostic tests are a scarce and finite resource, so abundance in one country can quickly lead to shortages in others, creating a competitive landscape. Countries experience peaks in infections at different times, meaning that the need for diagnostic tests also peaks at different moments. This phase lag implies opportunities for a more collaborative approach, although countries might also worry about the risks of future shortages if they help others by reallocating their excess inventory of diagnostic tests. This article features a simulation model that connects three subsystems: COVID‐19 transmission, the diagnostic test supply chain, and public policy interventions aimed at flattening the infection curve. This integrated system approach clarifies that, for public policies, there is a time to be risk‐averse and a time for risk‐taking, reflecting the different phases of the pandemic (contagion vs. recovery) and the dominant dynamic behavior that occurs in these phases (reinforcing vs. balancing). In the contagion phase, policymakers cannot afford to reject extra diagnostic tests and should take what they can get, in line with a competitive mindset. In the recovery phase, policymakers can afford to give away excess inventory to other countries in need (one‐sided collaboration). When a country switches between taking and giving, in a form of two‐sided collaboration, it can flatten the curve, not only for itself but also for others.