Two Celtic clans—the Garbh Clan and the Conchubhair Clan—are set to battle. (Pronounce them as you’d like; I don’t speak Gaelic.) According to tradition, the leader of each clan selects one warrior and the two warriors chosen engage in a fight to the death, the winner determining which will be the dominant clan. The three top warriors for Garbh are Bevan (which is Gaelic for “youthful warrior”), Cathal (strong in battle), and Duer (heroic). For Conchubhair, it is Fagan (fiery one), Guy (sensible), and Neal (champion). The leaders of the two clans know the following information about their warriors, and each knows that the other leader knows it, and furthermore, each leader knows that the other leader knows that the other leader knows it, and so forth (in other words, the game is common knowledge): Bevan is superior to Cathal against Guy and Neal, but Cathal is superior to Bevan against Fagan. Cathal is superior to Duer against Fagan, Guy, and Neale. Against Bevan, Guy is best. Against Cathal, Neal is best. Against Duer, Fagan is best. Against Bevan, Fagan is better than Neal. Against Cathal, Guy is better than Fagan. Against Duer, Guy and Neal are comparable. Assuming that each leader cares only about winning the battle, what can you say about who will be chosen to fight?