The earliest mention of gladiatorial combat dates from 310 BC but it was the Romans' Campanian (Capua) allies who used gladiators to celebrate a triumph over the Samnites. It is in Book IX of Livy's History. Books 11-20 are lost but there is a recap, called a Periochae, of Book XVI which notes that it was Decimus Junius Brutus who was the first to organize gladiatorial games to honor his father in 264. Again, the Romans were not loathe to borrow ideas from others.
Rome spent much of the rest of the 3d century at war with Carthage and given the hammer-and-tong nature of the fighting it is doubtful that they could have wasted much energy on public spectacles. Until 207 they were seriously in danger of losing the 2d Punic War. The Battle of the Metaurus turned that and in 202 was Zama and Carthage was done. But, up to then, the Romans had gotten their asses kicked multiple times by Hannibal if not so much by the other Carthaginian commanders.
Rome spent much of the rest of the 3d century at war with Carthage and given the hammer-and-tong nature of the fighting it is doubtful that they could have wasted much energy on public spectacles. Until 207 they were seriously in danger of losing the 2d Punic War. The Battle of the Metaurus turned that and in 202 was Zama and Carthage was done. But, up to then, the Romans had gotten their asses kicked multiple times by Hannibal if not so much by the other Carthaginian commanders.