The article discusses how different outcomes can occur in situations where multiple parties share limited resources. By using a mathematical approach, the researchers found that having a specific type of starting point can lead to multiple possible solutions. They also discovered that the elasticity of marginal utility plays a crucial role in determining whether a unique solution exists. If the elasticity meets a certain condition, a single solution is likely, but if it doesn't, multiple solutions can arise. This information can help understand and predict outcomes in scenarios like the tragedy of the commons.