Staffing Talk's Game Theory Contest award went to Kevin Prow, a TempWorks employee, who came up with the mathematically correct answer: in a world of logical and non-suicidal entities (staffing companies), one would only pounce if there were an even number of remaining entities. The logic being that if there were one or any odd number of remaining entities, it would devour the pouncer.
We received two other answers which lacked the math but more than made it up with creativity. The first sent along an image to convey the notion that the smallest will go for the marginal contract and then get eaten up by the largest:
Another commented that yes at least one needy, low-balling, dollar-exchanging, whoring staffing company out there would jump at the marginal contract regardless of the long-term consequences and that only by resolutely avoiding neediness can a staffing company survive.