# Consider an evolutionary version of the game between Baker and Cutler, from Exercise U1 of Chapter..

Consider an evolutionary version of the game between

Baker and Cutler, from Exercise U1 of Chapter 10. This time Baker and Cutler

are not two individuals but two separate species. Each time a Baker meets a

Cutler, they play the following game. The Baker chooses the total prize to be

either $10 or $100. The Cutler chooses how to divide the prize chosen by the

Baker: the Cutler can choose either a 50:50 split or a 90:10 split in the

Cutler’s own favor. The Cutler moves first, and the Baker moves second. There

are two types of Cutlers in the population: type F chooses a fair (50:50)

split, whereas type G chooses a greedy (90:10) split. There are also two types

of Bakers: type S simply chooses the large prize ($100) no matter what the Cutler

has done, whereas type T chooses the large prize ($100) if the Cutler chooses a

50:50 split, but the small prize ($10) if the Cutler chooses a 90:10 split. Let

f be the proportion of type F in the Cutler population, so that (12 f )

represents the proportion of type G. Let s be the proportion of type S in the

Baker population, so that (12 s) represents the proportion of type T.

(a) Find the fitness of the Cutler types F and G in terms

of s.

(b) Find the fitness of the Baker types S and T in terms

of f.

(c) For what value of s are types F and G equally fit?

(d) For what value of f are types S and T equally fit?

(e) Use the answers above to sketch a graph displaying

the population dynamics. Assign f as the horizontal axis and s as the vertical

axis.

(f) Describe all of the equilibria of this evolutionary

game, and indicate which ones are stable.