Pike in the Enchanted Pond

An enchanted pond holds $33$ pike and $1$ minnow. The pond's magic keeps every fish fed indefinitely, so nothing must eat — but any pike would happily eat the minnow, except for the curse: the moment a pike eats the minnow, that pike transforms into a minnow itself (and could then be eaten by another pike). All pike are perfectly rational, know the rules, and value their own survival above the pleasure of eating. What is the stable outcome — how many pike and how many minnows remain?