On average, who has the advantage - a fugitive or his pursuer?
Is this an actual riddle with an answer? or just a bit of game theory speculation?
I would think it depends highly on circumstance. But cutting through the various possibilities to consider what you might call the "average" chase where the fugitive is by default considered to be leaving some from of "trail" then I would say the persuer would seem to have the advantage.
If the fugitive flees quickly and hastily they will leave a more distinct trail which the persuer can follow more easily and at a more leasurely pace anticipating that fugitive will eventually have to stop to rest and, at a minimum, lose the greater portion of their lead.
If the fugitive takes their time to minimize the trial left behind the persuer may decide to make a small gamble by increasing their pace to some small degree slowly and continually cutting into the fugitives lead over the course of the chase.
Any attempt at a major disruption of the trail by the fugitive comes at great cost to their lead and is at best a gamble, riskier the more time and effort is invested in the excersize. In the end it is unlikely that the fugitive will lose their persuer completely and will still be persued regardless of the lead gained.
The primary advantage for the persuer seems to be strategy based on knowledge from the trail of the persued while the persued is strategizing blindly.
Thank you, Stat. Game theory it is.
It came to me upon reading your response that two debaters may alternate between the roles of fugitive and pursuer, but much preferring the latter.
As a matter of uncertainty, the fugitive is definitely at a disadvantage. Even with random relative separation, given a large enough elapse of time, they will be caught.
Recall the saying: "Wait in Times Square and eventually everyone you know will pass."
The one I heard was "Wait by the river long enough, and the bodies of your enemies will float by."
Let's use math. Assume that the fugitive is fleeing with an average velocity v. While fleeing, he leaves behind a trail with a 'detectability rating' t(v) (t for trail). What this means is irrelevant, but t is an increasing function The pursuer is going to travel at a velocity w. While traveling at this speed, he can detect trails of at least strength d(w) (d for detect). d is also an increasing function So we have two conditions:
1) w>v is necessary for the pursuer to win
2) d(w)<t(v) is necessary for the pursuer to track his target
So the fugitive has the advantage as long as there exists v such that d(v)>t(v) and heuristically, the fugitive should escape nearly every time. Of course, in practice d is often much smaller than t (for example, if you have a helicopter and you're traveling behind the fugitive in a car, d is zero and will continue to be zero). So now it comes down to pure experimentation to determine the values of d and t
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