Ana, Bernardo and Carlos find an enchanted lamp. The genie of the lamp offers them a kilo of gold but tells them that they must divide it among themselves in the following way: In the first period Ana makes an offer (what proportion of the kilo of gold each one keeps) and then Bernardo and Carlos decide whether to accept or reject it (simultaneously). If both accept, the game ends and they divide the kilo of gold according to the offer. If at least one player declines, Bernardo makes an offer again and then Ana and Carlos decide whether to accept or reject (simultaneously). If both accept, the game ends. If either of them declines, then Carlos makes a counteroffer. If both accept, the game ends and they divide the kilo of gold according to the offer. If at least one player rejects, they are left without the kilo of gold because the genius gets furious for not agreeing. The discount factor is a, b and c for Ana, Bernardo and Carlos respectively.

Please answer the following question:

(a) Represent the game in the extensive form