Final answer:
Gladiatorial combat was a game played in both Ancient Rome and the medieval period, evolving from funeral rites to public entertainment and influencing medieval tournament combat.
Step-by-step explanation:
The game that was played in both Ancient Rome and medieval times is likely to be a form of gladiatorial combat. While the exact nature of the contests would have evolved over time, the fundamental concept of armed combat for sport has a long history. In Ancient Rome, gladiatorial games began as part of funeral rites and grew to become a major form of public entertainment. These spectacles could include a variety of events, from one-on-one combat to large-scale battles reenactments. Gladiatorial combat retained its popularity through the end of the Roman Empire, and its influences were seen in the medieval period, where forms of tournament combat emerged, including jousting.