Sure, here is a detailed explanation of the correct matches:

I. Mrichchakatikam - Shudraka: This is a correct match. "Mrichchakatikam," also known as "The Little Clay Cart," is a Sanskrit play attributed to the playwright Shudraka. It is one of the earliest surviving Indian dramas.

II. Buddhacharita - Vasuvandhu: This is not a correct match. The "Buddhacharita" is an epic poem written by Ashvaghosha, not Vasuvandhu. Ashvaghosha was a Buddhist philosopher and poet, known for his contributions to Buddhist literature.

III. Mudrarakshasa - Vishakhadatta: This is a correct match. "Mudrarakshasa" is a Sanskrit play attributed to the playwright Vishakhadatta. It is a historical drama based on the life of Chandragupta Maurya and the political events of his time.

IV. Harshacharita - Banabhatta: This is a correct match. "Harshacharita" is a biography of the Indian emperor Harsha, written by the court poet Banabhatta. It provides insights into the life and achievements of Emperor Harsha.

Therefore, the correct matches are I, III, and IV.