Interested readers can find some information on the traditions of dialectic and eristic in India in the following studies (scroll doewn for my comments on each of them and a tentative summary):

• Esther Solomon, Indian Dialectics. Methods of Philosophical Discussion (Ahmedabad: B.J. Institute of Learning and Research) 1976;
• Johannes Bronkhorst, “Modes of debate and refutation of adversaries in classical and medieval India: a preliminary investigation”, Antiquorum Philosophia 1 (2007), 269-280;
• Johannes Bronkhorst, “Does India think differently?”, in Denkt Asien anders? Reflexionen zu Buddhismus und Konfizianismus in Indien, Tibet, China und Japan, edited by Birgit Kellner and Susanne Weigelin-Schwiedrzik (Göttingen: Vienna University Press, 2009), 45–54;
• Sung Yong Kang, Die Debatte im alten Indien. Untersuchungen in der Carakasaṃhitā Vimānasthāna 8.15-28 (Reinbeck: Wezler 2003);
• Ernst Prets, “Theories of Debate in the Context of Indian Medical History: Towards a Critical Edition of the Carakasaṃhitā”, in Encyclopedia of Indian Wisdom. Prof. Satya Vrat Shastri felicitation volume, edited by Rāma Karaṇa Śarmā (Delhi: Bharatiya Vidya Prakashan 2005), 394-403;
• Bimal Krishna Matilal, “Debate and Dialectic in Ancient India”, in Philosophical Essays. Professor Anantalal Thakur Felicitation Volume, edited by Ramaranjan Mukherji (Calcutta: Sanskrit Pustak Bhandar, 1987), 53-66;
• Gerhard Oberhammer, “Ein Beitrag zu den Vāda-Traditionen Indiens”, Wiener Zeitschrift für die Kunde Süd- und Ost-Asiens 7 (1963), 63-103;
• Karin Preisendanz, “Debate and Independent Reasoning vs. Tradition: On the Precarious Position of Early Nyāya”, in Harānandalaharī. Volume in Honour of Professor Minoru Hara on his Seventieth Birthday edited by Ryutaro Tsuchida and Albrecht Wezler (Reibeck: Wezler 2000), 221-251;
• Ernst Prets, “Theories of Debate, Proof and Counter-Proof in the Early Indian Dialectical Tradition”, Studia Indologiczne 7 (2000), 369-382;
• Ernst Prets “Futile and False Rejoinders, Sophistical Arguments and Early Indian Logic”, Journal of Indian Philosophy 29.5 (2001), 545-558;
• Andrew Nicholson, Unifying Hinduism: Philosophy and Identity in Indian Intellectual History (New York: Columbia University Press, 2010).

Solomon’s book is a classic, although somewhat outdated reference book on the topic of dialectics in Nyāya and in other schools.
Among the other authors, Bronkhorst suggests that the roots of Indian dialectics should be placed in the Buddhist communities in the northwest of the Indian subcontinent (which might have been influenced by the Greek tradition of public debate in the Indo-Bactrian kingdoms). Kang and Prets (“Theories of Debate”) focus on the (indigenous) roots of dialectics in the medical tradition, where a discussion (called sambhāṣā ‘conversation’) among practitioners was meant to establish the truth about the patient’s condition through the evidence at hand (their symptoms), whereas the term vāda meant a hostile debate and included the subgroups of jalpa and vitaṇḍā). Oberhammer, Preisendanz, Prets and Nicholson focus on the early history of vāda and its more technical elements.
All of these scholars agree on the presence of hostile (‘agonistic’ in Nicholson’s book) and collaborative (‘non-agonistic’) forms of dialogue in pre-Classical and Classical Indian Philosophy, with the latter possibly having developed out of the former (see the Conclusions in Nicholson’s book).
B.K. Matilal (1935–1991), himself an analytic philosopher and a scholar of Indian logic and philosophy in general, performed a move similar to that of Daya Krishna, insofar as he focused on the epistemological potential of vāda (although, differently from Daya Krishna, he did not exploit the creativity of this concept in different contexts).