I think standard game theory applies here. If an agent isn’t hazed, does it prefer to haze or not? If it slightly prefers not-hazing, the only Nash equilibrium is the one where everyone hazes iff they were hazed. So if the chain has a beginning, then the first agent doesn’t haze (because it wasn’t hazed) and no one ever hazes anyone. But if there’s a slight preference for hazing, the only Nash equilibrium is the one where everyone hazes unconditionally. This discontinuity hints that your problem formulation is an unstable point. I don’t completely understand what this implies for UDT’s answer.
I think standard game theory applies here. If an agent isn’t hazed, does it prefer to haze or not? If it slightly prefers not-hazing, the only Nash equilibrium is the one where everyone hazes iff they were hazed. So if the chain has a beginning, then the first agent doesn’t haze (because it wasn’t hazed) and no one ever hazes anyone. But if there’s a slight preference for hazing, the only Nash equilibrium is the one where everyone hazes unconditionally. This discontinuity hints that your problem formulation is an unstable point. I don’t completely understand what this implies for UDT’s answer.