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The gladitorial games were largely thought to be adopted by the Campanians and found their way to Rome through the Etruscans. From this site:
Adopted from the earlier Etruscans, perhaps by way of Campania, gladiatorial games (munera) originated in the rites of sacrifice due the spirits of the dead and the need to propitiate them with offerings of blood. They were introduced to Rome in 264 BC, when the sons of Junius Brutus honored their father by matching three pairs of gladiators.
Also supported by the Wikipedia page on Gladitorial games.
However, various sites also espouse that the first Gladitorial games, which took place approximately 310 BC; almost fifty years before their appearance in Rome, did not originate in (what we now call) Italy at all. Rather they were of Greek origin.
In The Iliad, Homer relates how blood-games were held after Patroklos [] was slayed by Hector. While nobody got killed, the event was an offering of blood to facilitate the transition of Patroklos['s] spirit to the world of the dead. Researchers believe Home was describing a common ceremony in the funeral of important individuals. The participants in these events, though, were free men who volunteered to honor the dead. (see here)
In short, the origin of the Gladitorial games depends on your definition of what it meant to be a gladiator. In terms of funeral rites it seems the games were Greek in origin and based on the publication date of the epic poems by Homer were at least 1000 years old by the time they reached the Campania region in 264 BC.
However if your definition of the games is the bloody affairs conducted in the Colosseum where hundreds of men died in droves, that has a distinctly Roman history and probably began around 65 BC when Caesar sent around 320 pairs of gladiators to their deaths.