That sounds more like a free rider problem as opposed to tragedy of the commons- free riding being when one party invests the resources to attain a benefit that others thereafter can use for free.
Tragedy of the Commons is when there is a finite resource that a group of individuals all use, where increased individual use benefits the individual at the expense of the group. For instance, a popular example is that of a cow pasture shared by a group of farmers. The pasture can only support a certain number of cows, and going over that number renders the field barren. Each farmer has an individual interest in how many cows he can keep on the pasture- the more cows he has, the more money he makes. Therefore, each farmer, acting in his own self interest, will try and cram as many cows as he can on to the field, because he doesn't pay the price of putting another cow on, the group of farmers does. However, because there are now so many cows on the field due to all the farmers cramming cows onto the field, the pasture is now rendered barren, and everyone loses.
Getting somewhat off subject here, but necessity and demand are the parents of invention, IMO, not IP law. The market would still facilitate new inventions even without state granted monopolies because the inventing party is in the best position to exploit the new invention. While that would probably mean that the purchase of an initial invention might cost a bit more (as the inventor will want to be compensated for his creativity), it would ultimately drive down prices and might even increase the number of inventions available- after all, patent law prohibits one from using another's patented invention to invent something else without obtaining the permission of the original inventor to use his invention.