Step 1: Understanding the Concept:
This question asks for the author of the Sanskrit treatise 'Nītivākyāmṛtam'.
Step 2: Detailed Explanation:
Nītivākyāmṛtam ("The Nectar of Aphorisms on Polity") is a work on political science and ethics written in the 10th century CE. It presents a Jain perspective on statecraft, drawing upon earlier works like Kautilya's Arthaśāstra.
The author of this text was Somadeva Sūri, a prominent Digambara Jain monk, poet, and scholar.
Let's consider the other authors listed:
1. Bhartṛhari: A 5th-century grammarian and poet, famous for the \textit{Vākyapadīya} (on grammar and linguistic philosophy) and the \textit{Śatakatraya} (three collections of hundred verses).
2. Kāmandaka: Author of the \textit{Nītisāra}, another important text on polity that is considered a summary of Kautilya's Arthaśāstra.
4. King Bhoja: The 11th-century Paramara king of Dhara, a great polymath credited with numerous works on a wide range of subjects, but not the Nītivākyāmṛtam.
Step 3: Final Answer:
The author of 'Nitivākyāmṛtam' is Somadeva Suri. Therefore, option (3) is correct.