3. Player 1 is seeking to get a project approved by Antalya Belediyesi, which will require bribing a few officials. Three officials are relevant to the approval process: players 2, 3, and 4. Player 1 has access to player 2, while player 2 has access to players 3 and 4. In stage 1, player 1 offers a bribe to player 2, denoted b2, which is any integer from {0,1,...,100}. The bribe is of the form: "If the project is approved, 1 then I'll pay you by." In stage 2, player 2 accepts or rejects the bribe. If he rejects it, then the project is not approved and the game is over. If player 2 accepts the bribe (which, recall, is paid only if the project is eventually approved), then the game moves to stage 3, which has player 2 simultaneously offer bribes to player 3 and 4, which are denoted by and be respectively. b3 and b4 are any integers from {0, 1, ..., by} for which their sum does not exceed ba; thus, player 2 can offer bribes financed by the bribe given to him by player 1. In stage 4, players 3 and 4 each decide whether to accept or reject the bribe made to him by player 2. If both players 3 and 4 reject the bribes, then the project is not approved, no bribes are paid to any players, and the game is over. If, out of players 3 and 4, at least one player accepts a bribe, then the project is approved and all bribes are paid to those players who accepted bribes. Player 1's payoff is 0 when the project is not approved and is 100 minus the bribe paid to player 2 when the project is approved. For player 2, if the project is not approved, then his payoff is 4.5; if the project is approved, then it equals the bribe he received from player 1 less the bribes he paid to players 3 and 4. For player 3, his payoff equals 9.5 when the project is not approved and/or he rejected the bribe, and equals the bribe he was offered when the project is approved and he accepted the bribe. The same applies to player 4 as well. Using SPNE, is the project approved, and, if so, what bribes are given out? (20 Marks)