Wild India: Elephant Fights
Elephants test their strength with each other and then remember these victories and defeats which help them assess their rivals in future battles. Elephants often come in conflict with each other when they aspire to mate with the same female elephant. These jostling also helps them learn tactics for future battles. If an elephant misses a trick then the other can just gore it with its tusk.
During these battles, the elephants often bite each others tail and as a result one finds elephants with broken tails. One can see that behaviour in this video of Asiatic Elephants pushing and shoving each other. This was filmed in Kaziranga National Park, India.