Step 1: Concept Identification:
The question requires identification of the author of the Sanskrit treatise 'Nītivākyāmṛtam'.
Step 2: Detailed Analysis:
Nītivākyāmṛtam (meaning "The Nectar of Aphorisms on Polity") is a 10th-century CE treatise on political science and ethics, reflecting a Jain viewpoint on statecraft and referencing earlier works like Kautilya's Arthaśāstra.
The author is identified as Somadeva Sūri, a notable Digambara Jain monk, poet, and scholar.
Evaluation of alternative authors:
1. Bhartṛhari: A 5th-century grammarian and poet, known for \textit{Vākyapadīya} (grammar/linguistic philosophy) and \textit{Śatakatraya} (three sets of hundred verses).
2. Kāmandaka: Authored the \textit{Nītisāra}, another significant text on polity, considered a summary of Kautilya's Arthaśāstra.
4. King Bhoja: An 11th-century Paramara king of Dhara, a polymath with numerous works across various subjects, but not the author of Nītivākyāmṛtam.
Step 3: Conclusion:
Somadeva Suri is the author of 'Nitivākyāmṛtam'. Consequently, option (3) is correct.