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.