The Chicken, aka Hawk/Dove game, is a pain in the neck to analyze from a “naive decision theory” perspective.
Level Zero analysis:
The best response to Dove is Hawk. If my opponent is going to play Dove, I want to play Hawk.
The least bad response to Hawk is Dove. If my opponent is going to play Hawk, I want to play Dove.
Going meta:
If I can predict that my opponent plays Dove in response to HawkBot, I want to self-modify into HawkBot and trap them in the Nash equilibrium that’s good for me.
If my opponent is HawkBot, I want to yield and play Dove.
Going more meta:
If my opponents predict that I’ll play Dove in response to HawkBot, then they’ll self-modify into HawkBot and trap me in the Nash equilibrium that’s bad for me. So I don’t want to play Dove in response to HawkBot. But if I play Hawk in response to HawkBot, I’m basically HawkBot myself, and the HawkBot vs HawkBot matchup leads to the worst outcome possible. So it can’t be right to play Dove, and it can’t be right to play Hawk either.
Which leaves me with only one possible conclusion:
The Chicken, aka Hawk/Dove game, is a pain in the neck to analyze from a “naive decision theory” perspective.
Level Zero analysis:
The best response to Dove is Hawk. If my opponent is going to play Dove, I want to play Hawk.
The least bad response to Hawk is Dove. If my opponent is going to play Hawk, I want to play Dove.
Going meta:
If I can predict that my opponent plays Dove in response to HawkBot, I want to self-modify into HawkBot and trap them in the Nash equilibrium that’s good for me.
If my opponent is HawkBot, I want to yield and play Dove.
Going more meta:
If my opponents predict that I’ll play Dove in response to HawkBot, then they’ll self-modify into HawkBot and trap me in the Nash equilibrium that’s bad for me. So I don’t want to play Dove in response to HawkBot. But if I play Hawk in response to HawkBot, I’m basically HawkBot myself, and the HawkBot vs HawkBot matchup leads to the worst outcome possible. So it can’t be right to play Dove, and it can’t be right to play Hawk either.
Which leaves me with only one possible conclusion: