Polypoly is used less frequently than monopoly. That occurs mainly in the context of economics, where it describes a situation in which there are many small sellers but no large ones. If polypoly is also often used as synonym for oligopoly (see Jay’s comment on your question), consider comparing polypropy to oligopoly or unipropy.

Because its meaning is liable to be confused in this way, polypoly is not a good general antonym for monopoly. Because the word anti-multipoly is not real, what does it mean? ‘) In addition to Jay’s suggestions given above, you might consider describing the situation as competitive or as one of free competition.

As a side note, you can often get a sense of a word’s scarcity by using Google Ngrams, which chart the frequency of a word’s use in a book over a period of time. This one shows how often monopoly occurs in books written between 1900 and 2000. This is because polypoly is extremely rare compared to bipoly, while multipoly is rarer still.