There are many occasions in history when the world comes together to compete in sporting events (The Olympics, World Cup, etc.). These events have many reasons for existing, of course, but the end result is that teams or individuals who differ ideologically come together to compete in sport. How might such an event be held in your current (or past) works of fiction? Describe what you’ve done in your works here in the comments, or put together a quick paragraph or two giving an example of how sports or other competitive events (spelling bees or chess matches, for example) might level the playing field amongst your characters and their societies.
Today's Author 
In high school, I wrote a series of stories called “Par Wars”. Aside from the cheap and obvious movie reference, one of the key elements of the stories was the Intergalactic Olympics and the most important event of them: Space Golf. Space Golf involved knocking variously-sized and shaped space rocks into artificial black holes. The rocks would be in orbit around a planet or moon, the black holes set a certain distance away. Competitors used their physical skills as well as their knowledge and understanding of the Laws of Gravity to get the better of their foes in the game.
In the first story, Space Golf ended a long and bloody war. In the second installment, “Drunk Driving Can Kill a Friendship”, poor decisions related to the game actually started a war (as you might guess, alcohol was involved). In the third installment, “May the Sports Be With You”, there is a deep, dark secret uncovered where one world is gaming the system as it were, leading to all kinds of trouble. Then in the fourth installment, “Exiles of the Treasonous and Corrupt”, Space Golf solves more intergalactic misery, but it can’t heal the rifts between individual characters.
High quality literature? No way. Fun to write? Absolutely. I’ve actually been planning on a fifth installment for some time now, but simply haven’t been able to go about writing it. This series is one of my early and highly unedited sets of works and it is something I’ve considered going back to rewrite in some fashion. Partly because of how fun it was to write it but also because I have former teachers as well as friends from high school who keep asking me about it!