Consider a survival game in which members of a large population of animals meet in pairs 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 purpose 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 caloricintake determines each player's 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 get the food or to lose and get no food. i. Draw the payoff table for the game played between two random players from this population.

ii. Find all the evolutionarily stable strategies in the population. Check for pure strategies as well as mixed strategies.

iii. 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. As before, assume that when two fighters meet, each is equally likely to win the fight and get the food or to lose and get no food.

i.Draw the payoff table for the game played between two random players from this population.

ii.Find all the evolutionarily stable strategies in the population. Check for pure strategies as well as mixed strategies.

iii.What type of game is being played in this case?