Consider a survival game in which a large population of
animals meet and either fight over or share a food source. There are two
phenotypes in the population: one always fights, and the other always shares.
For the purposes of this question, assume that no other mutant types can arise
in the population. Suppose that the value of the food source is 200 calories
and that caloric intake determines each player’s reproductive fitness.
If two sharing types meet one another, they each get half
the food, but if a sharer meets a fighter, the sharer concedes immediately, and
the fighter gets all the food.
(a) Suppose that the cost of a fight is 50 calories (for
each fighter) and that when two fighters meet, each is equally likely to win
the fight and the food or to lose and get no food. Draw the payoff table for
the game played between two random players from this population. Find all of
the ESSs in the population. What type of game is being played in this case?
(b) Now suppose that the cost of a fight is 150 calories
for each fighter. Draw the new payoff table and find all of the ESSs for the
population in this case. What type of game is being played here?
(c) Using the notation of the hawk–dove game of Section
12.6, indicate the values of V and C in parts (a) and (b), and confirm that
your answers to those parts match the analysis presented in the chapter.