# Recall Exercise S7. Hares, it turns out, are very impolite winners. Whenever hares race tortoises,..

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?

Explain.

(f) Will the polymorphic equilibria found to exist in

part (e) be stable? Why or why not?