The Honda Amaze is sold in India below the Honda city. In INR here's the approximate comparison.
Amaze - INR 5,00,000
City - INR 8,00,000
Civic - IN 13,00,000
It competes against the Suzuki Swift DZire (sedan based on Swift), Hyunday XCent , Tata Tigor. The Suzuki is king in this segment.
This is an entry level segment for sedans. India gives tax benefits for cars smaller than 4 meters in length and these cars were all designed to be sub-4 meter sedans. Ergo, they can sell as a sedan (considered premium in India) at a lower cost. As a result the primary objective is space optimization and cost competitiveness.
In India the cost-sensitive is also sensitive to post-purchase costs where Suzuki and Hyundai are much, much better.
Honda City is a big player in its less price-sensitive segment. The Amaze by comparison hasn't sold well.