Consider a survival game in which a large population of animals meet andeither fight over or share a food source. There are two phenotypes in thepopulation: one always fights, and the other always shares. For the purposesof this question, assume that no other mutant types can arise in thepopulation. Suppose that the value of the food source is 200 calories andthat caloric intake determines each player's reproductive fitness. If twosharing types meet one another, they each get half the food, but if a sharermeets a fighter, the sharer concedes immediately, and the fighter gets allthe food.(a) Suppose that the cost of a fight is 50 calories (for each fighter) and thatwhen two fighters meet, each is equally likely to win the fight and thefood or to lose and get no food. Draw the payoff table for the gameplayed between two random players from this population. Find allof the ESSs in the population. What type of game is being played inthis 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 inthis case. What type of game is being played here? ' ·(c) Using the notation of the Hawk-Dove game of Section 13.6, indicate thevalues of Vand Cin parts (a) and (b) and confirm that your answers tothose parts match the analysis presented in the chapter.