Question

Recall the Lions and Antelopes game. This time there are two lions and three antelopes. The sizes (values) of the antelopes are A1 > A2 > A3. As before, if two lions chase the same antelope they each get half. If they chase different antelopes they each get the one they chase.

(a) Write down the game payoff matrix.

(b) Show that if A2 < A1/2 then chasing antelope 1 is an ESS.

(c) Now suppose A2 > A1/2 and A3 is very small. Show there is a p ∈ (0, 1) so that σ = (p, 1 − p, 0) is an ESS.

(d) Again, A2 > A1/2. Find a threshold, v, in terms of A1 and A2 so that if A3 < v then strategy 3 cannot invade σ, and if A3 > v then it can.

(e) What happens if A3 = v?

Answer 1