Placing emphasis on ‘noticing vs running’ is just confusing you. Noticing helps the rabbit run just as much as it helps it look in the right direction.
Sorry I wasn’t being clear, previously I had always meant noticing==‘showing the fox you have noticed it’.
If average rabbit speed become slower then there will be a commensurate change in the threshold at which foxes chase rabbits even when they have been spotted.
What threshold? I’m guessing other factors such as the fox’s independent assessment of the rabbit’s speed?
It will remain useful to show the fox that it has been spotted in all cases in which about 200ms of extra head start is worth sacrificing so that a chase may potentially be avoided.
I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?
consider a situation in which rabbits and foxes always become aware of each other’s presence at a distance of precisely 250m. Would anyone suggest that rabbits would freeload and not bother to be fast themselves in that circumstance?
What threshold? I’m guessing other factors such as the fox’s independent assessment of the rabbit’s speed?
If the average rabbit becomes slower then the average fox will be more likely to estimate that a given rabbit chase is successful.
I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?
Not particularly. We haven’t been quantising anyway and it reasonable to consider the overhead here negligible for our purposes. ′
I don’t understand this part.
You don’t particularly need to. Just observe that rabbits running fast to avoid foxes is a stable equilibrium. Further understand that nothing in this scenario changes the fact that running fast is a stable equilibrium. The whole ‘signalling makes the equilibrium unstable’ idea is a total red herring, a recipe for confusion.
Sorry I wasn’t being clear, previously I had always meant noticing==‘showing the fox you have noticed it’.
What threshold? I’m guessing other factors such as the fox’s independent assessment of the rabbit’s speed?
I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?
I don’t understand this part.
If the average rabbit becomes slower then the average fox will be more likely to estimate that a given rabbit chase is successful.
Not particularly. We haven’t been quantising anyway and it reasonable to consider the overhead here negligible for our purposes. ′
You don’t particularly need to. Just observe that rabbits running fast to avoid foxes is a stable equilibrium. Further understand that nothing in this scenario changes the fact that running fast is a stable equilibrium. The whole ‘signalling makes the equilibrium unstable’ idea is a total red herring, a recipe for confusion.