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"grabbing one of these super marathon runners, taking him to the wide open plains of Utah, and asking him to bring back a dead antelope."

you might need a tracker for when the antelope goes over the horizon/out of sight. Most ong distance runners would be clueless about tracking prey. Maybe the tracker can drive/cycle alongside the runner in a hypothetical experiment.

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I suppose darting the antelope first and attaching a radio direction beacon would be cheating.

"darting the antelope first and attaching a radio direction beacon"

well, If you don't want to model how much the hunter recovers during periods of relative rest ( slower-than-running-time-spent-in-tracking this would be additional resting time for the prey as well I suppose) you could do it that way.

Does anyone in HN know of what kind of mathematics would be needed to set up a simulation like this?equations for rates of exhaustion/ speed loss over time etc?

You can easily model something like this with regular old ordinary differential equations in Mathematica or MATLAB. The hard part would be gathering the data to design realistic equations.

Rather than mathematics, you could try using a multi-agent model. Set up a set of "rules" each party follows and give it a go.

NetLogo is something i've used before to do similar stuff.

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