Competition is all around us, from sporting events to how many ads you see for a particular product. Composers haven't been insulated from competition, either. When Joseph Haydn was working in London, his former student Ignaz Pleyel showed up and became his teacher's rival. Haydn decided he would write a Sinfonia Concertante, like Pleyel's (who had already written 4 of his 6). This hybrid music would combine elements of a concerto (a soloist or group of soloists and orchestra) and a symphony. Haydn only wrote one, but it has become one of his most beloved works.
Do you know what Pleyel is mainly known for today? Pianos.
(Chopin's favorite piano was a Pleyel)