No, there are really tangential analogies about how self-interested behavior can have negative consequences, but it is and has always been based around a bunch of numerous myths. Externalities is a better description of this.

Elinor Ostrom investigated management of the commons and the original description of tragedy of the commons was a complete lie. The commons were enclosed so that in this transitional stage of feudal lords could become businessmen that could profit off of using the land rather than taxing a peasant community living off of it. The enclosed commons is an asset to generate profit, where if enough of an increase in profit could be achieved, that could be reinvested, meant that exhausting the land would be an economically rational strategy. Where, if a peasant community is using it to sustain themselves, they have to carefully manage and steward that land so it is still producing for themselves years later, their children, and their grandchildren. The complete opposite of what the "tragedy of the commons" describes.