Problem # 3. (20pt) Consider the pairwise competition for scarce resources among members of a species. There are two genetic types: Aggressive and passive. When two aggresives engage, they fight and the winner gets 10 points for the resource. The loser gets -20 for the bodily damage. When a passive and an aggressive engage, aggressive gets the resource (10 points), passive gets nothing (0 points). When two passives engage they wait for a long time who will get the resource (they both lose 1 points for the lost time and energy) and then one of them gets the resource (10 points). a) (5 pt) Write the expected payoff matrix of this game. b) (15 pt) Suppose that this population has achieved its evolutionary balance (which depends on the availability of resources), i.e., game-theoretic equilibrium. What per- centage of the population is passive? Problem # 3. (20pt) Consider the pairwise competition for scarce resources among members of a species. There are two genetic types: Aggressive and passive. When two aggresives engage, they fight and the winner gets 10 points for the resource. The loser gets -20 for the bodily damage. When a passive and an aggressive engage, aggressive gets the resource (10 points), passive gets nothing (0 points). When two passives engage they wait for a long time who will get the resource (they both lose 1 points for the lost time and energy) and then one of them gets the resource (10 points). a) (5 pt) Write the expected payoff matrix of this game. b) (15 pt) Suppose that this population has achieved its evolutionary balance (which depends on the availability of resources), i.e., game-theoretic equilibrium. What per- centage of the population is passive