Which author was an American dramatist whose novel The Death of a Salesman won the Pulitzer during post-modernism period?

There seems to be a misunderstanding in your question. The period during which Arthur Miller's play "Death of a Salesman" was written and awarded the Pulitzer is not considered the postmodern period but rather modernism. Postmodernism emerged as a significant cultural and intellectual movement primarily during the latter half of the 20th century. Arthur Miller lived from 1915 to 2005, and "Death of a Salesman" was published in 1949, making it a prominent work of the modernist literary era.