This sort of play is the "I'm bigger" game, ritualized play between two males. I am very sorry I entered it, because people don't know horses enough to recognize it as a game. Males will play this as adults, it's not just a juvenile game. It's sort of like thumb wrestling, only with head and necks, no other "fingers" to interfere, and the goal is to be on top. It often ends with both parties rearing, to really be "bigger". Then they start over.
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