A pirate ship (P) wishes to capture a yacht (Y) that is leaving port for open water and steal from its passengers. There is also 3 Coast Guard (C) boat that will patrol the local area. There are two ways that Y can reach open water from its dock: Government Cut (G) and Haulover Inlet (H). Simultaneously and independently, Y chooses which inlet to use, and P chooses at which inlet to wait to ambush Y, and C chooses which inlet to patrol. That is, the three players simultaneously and independently choose between G and H. elf C chooses the same location as P, C apprehends P. This results in a payoff of 140 to C and 140 to P. If Y is also at the same location, C's presence prevents P from capturing Y. This is the only payoff relevance of C's choice for Y. lf C does not apprehend P, C's payoff is 0. Additionally, C's payoff is not inuenced by Y's choice. If Y and P choose the same inlet and C chooses a different one, P captures Y, resulting in a payoff of -140 for Y and 140 for P. If not captured, Y's payoff is 0. If P does not capture Y and is not apprehended by C, P's payoff is 0. Find a mixed-strategy Nash equilibrium of this game. Let p, q, and r denote the probability with which P, Y, and C, respectively, play G. Please show any calculations used. k