There are two types of racers—tortoises and hares—who race against one another in randomly drawn…

There are two types of racers—tortoises and hares—who
race against one another in randomly drawn pairs. In this world, hares beat
tortoises every time without fail. If two hares race they tie, and they are
completely exhausted by the race. When two tortoises race they also tie, but
they enjoy a pleasant conversation along the way. The payoff table is as
follows (where c . 0):

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(a) Assume that the proportion of tortoises in the
population, t, is 0.5. For what values of c will tortoises have greater fitness
than hares?

(b) For what values of c will tortoises be fitter than
hares if t = 0.1?

(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 have greater fitness 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.

 

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