There are two power brokers tasked with the job to win over a government official who is known to be corrupt. Each broker wants the official to do them a favor of value privately known to them but commonly known to be uniformly distributed over the interval [0, k]. Each lobbyist broker chooses to win over the official by bribing him with an expensive gift. The government official can grant only one favor at a time. He gets to keep both the gifts but he will choose to do a favor to that broker who bribes him the most.

(a) Find the optimization problem of the brokers and their equilibrium bidding strategy.