Recall Exercise S7. Hares, it turns out, are very
impolite winners. Whenever hares race tortoises, they mercilessly mock their
slow-footed (and easily defeated) rivals. The poor tortoises leave the race not
only in defeat, but with their tender feelings crushed by the oblivious hares.
The payoff table is thus:
(a) For what values of c are tortoises fitter than hares
if t, the proportion of tortoises in the population, is 0.5? How does this
compare with the answer in Exercise S7, part (a)?
(b) For what values of c are tortoises fitter than hares
if t 5 0.1? How does this compare with the answer in Exercise S7, part (b)?
(c) If c 5 1, will a single hare successfully invade a
population of pure tortoises? Explain why or why not. (d) In terms of t, how
large must c be for tortoises to be fitter than hares?
(e) In terms of c, what is the level of t in a
polymorphic equilibrium? For what values of c will such an equilibrium exist?
(f) Will the polymorphic equilibria found to exist in
part (e) be stable? Why or why not?