Two lions see a big impala and a little impala in the distance. Each lion independently chooses which impala to chase. The lions will kill whichever impala they chase, but if they choose the same impala, they will have to share it. The value of the big impala is 4, the value of the little impala is 2. The payoff matrix is thenlion 2 big littlelion 1 big (2,2) (4,2)little (2,4) (1,1)Our classification of 2 × 2 symmetric games (Theorem 8.5) does not apply to this one because a = c.(1) Are there any strictly dominated or weakly dominated strategies?(2) Find the pure strategy Nash equilibria.(3) Check whether any pure strategy symmetric Nash equilibria that you found in part (b) correspond to evolutionarily stable states.(4) Denote a population state by σ = p1b + p2l. Find the replicator system for this game. Answer: p˙1 = p1(2p1 + 4p2 − (p1(2p1 + 4p2) + p2(2p1 + p2))), p˙2 = p2(2p1 + p2 − (p1(2p1 + 4p2) + p2(2p1 + p2))).(5) Use p2 = 1 − p1 to reduce this system of two differential equations to one differential equation in the variable p1 only. Answer: p˙1 = 3p1(1 − p1) 2 .(6) Sketch the phase portrait on the interval 0 ≤ p1 ≤ 1, and describe in words what happens