This is the political shape of the whole chapter, and the second sentence explains the first.
Why no one could win. The three great powers of the Tripartite Struggle were evenly matched in exactly the three things that decide a long war:
- Military strength. The Rāṣhṭrakūṭas had “innumerable” troops and elephants (Al-Masūdī); the Gurjara-Pratīhāras had the finest cavalry in India (Sulaiman); the Pālas ruled “much of eastern and northern India”. No one had a weapon the others lacked.
- Administrative systems. All of them ran the same machinery — direct rule at the core, sāmantas beyond it, provinces, districts and self-governing villages. So none could out-govern the others or raise revenue faster.
- Strategic approaches. All three wanted the same prize for the same reasons, and all three could reach it. Look at Fig. 3.3 again — Kannauj lies open to west, east and south.
The evidence that it stayed a draw. The three “repeatedly warred against each other, with fluctuating outcomes and no lasting victor”. The Rāṣhṭrakūṭas briefly occupied Kannauj and later destroyed it — and even that only “hastened the disintegration” of the Pratīhāras without making the Rāṣhṭrakūṭas masters of the north.