I think the “conditional threat” thing might be a feature, not a bug.
Let’s say Alice owns a plot of valuable farmland, and Bob is very good at farming. To begin with, let’s say that Alice cannot defend her land at all. Bob can farm Alice’s land and gain 100 utils. Alternatively, he can do nothing, letting Alice farm poorly on her land and gain 10 utils. Bob is the only one here with a choice, and his argmax is on the pareto frontier, so he does it. Bob gets 100. Alice gets 0.
Now, let’s say that Alice can defend her land, which turns the “Bob farms” option into −100 utils for him (and still 0 for Alice). Then, if Alice goes first, she can do that, and Bob’s argmax is to let her farm for 10. Bob says “let’s do something else which is not that” and pays Alice 10 utils to let him farm. Bob gets 90, Alice gets 10. If Bob goes first, he farms, since he knows that Alice won’t kill him, so ROSE has 95 utils for Bob and 5 for Alice. If Alice can still farm the land herself after killing Bob, ROSE says Bob gets 90 and Alice gets 10.
This is Alice gaining a conditional threat and winning from it, but it makes perfect sense. The ability to kill trespassers (or follow through on lesser conditional threats against them) is sort of what makes the land Alice’s in the first place! Also, ROSE prevents Alice from rent-seeking beyond her BATNA where she inefficiently farms her land (even if she gains the option to simply kill Bob no matter what (-100 Bob, 0 Alice), which would shift CoCo and Nash to Bob farming and giving all of the gains to Alice). I think this is all desirable.
I think the “conditional threat” thing might be a feature, not a bug.
Let’s say Alice owns a plot of valuable farmland, and Bob is very good at farming. To begin with, let’s say that Alice cannot defend her land at all. Bob can farm Alice’s land and gain 100 utils. Alternatively, he can do nothing, letting Alice farm poorly on her land and gain 10 utils. Bob is the only one here with a choice, and his argmax is on the pareto frontier, so he does it. Bob gets 100. Alice gets 0.
Now, let’s say that Alice can defend her land, which turns the “Bob farms” option into −100 utils for him (and still 0 for Alice). Then, if Alice goes first, she can do that, and Bob’s argmax is to let her farm for 10. Bob says “let’s do something else which is not that” and pays Alice 10 utils to let him farm. Bob gets 90, Alice gets 10. If Bob goes first, he farms, since he knows that Alice won’t kill him, so ROSE has 95 utils for Bob and 5 for Alice. If Alice can still farm the land herself after killing Bob, ROSE says Bob gets 90 and Alice gets 10.
This is Alice gaining a conditional threat and winning from it, but it makes perfect sense. The ability to kill trespassers (or follow through on lesser conditional threats against them) is sort of what makes the land Alice’s in the first place! Also, ROSE prevents Alice from rent-seeking beyond her BATNA where she inefficiently farms her land (even if she gains the option to simply kill Bob no matter what (-100 Bob, 0 Alice), which would shift CoCo and Nash to Bob farming and giving all of the gains to Alice). I think this is all desirable.