Imagine we have a 3-player game. All payoffs described in the game will include the three...

Transcribed Image Text:

Imagine we have a 3-player game. All payoffs described in the game will include the three players, with the first payoff being for player 1, the second one being for player 2, and the third for player 3. Player 1 plays first, either A, B, or C. If Player 1 plays A, then Player 2 plays either X or Y, and they get the following payoffs: P2 P1 P1 A If Player 1 plays B, then Player 3 plays either X or Y, and they get the following payoffs: P3 P2 B X 1.4.6 X Y X 3.5.1 If Player 1 plays C, then Player 2 and Player 3 play the following game, with Player 2 moving first: Y 2.5, 10 X 1,4, 2 1,2,1 P3 Y 4.8.3 Y 1,3,7 3.1.1 1. (6 PTS) Draw the game tree for this game. Include nodes, strategies, and who makes decisions. 2. (6 PTS) Solve for the subgame perfect Nash equilibrium (Nash equilibrium for sequential game). (Hint: count how many nodes each player has.) Imagine we have a 3-player game. All payoffs described in the game will include the three players, with the first payoff being for player 1, the second one being for player 2, and the third for player 3. Player 1 plays first, either A, B, or C. If Player 1 plays A, then Player 2 plays either X or Y, and they get the following payoffs: P2 P1 P1 A If Player 1 plays B, then Player 3 plays either X or Y, and they get the following payoffs: P3 P2 B X 1.4.6 X Y X 3.5.1 If Player 1 plays C, then Player 2 and Player 3 play the following game, with Player 2 moving first: Y 2.5, 10 X 1,4, 2 1,2,1 P3 Y 4.8.3 Y 1,3,7 3.1.1 1. (6 PTS) Draw the game tree for this game. Include nodes, strategies, and who makes decisions. 2. (6 PTS) Solve for the subgame perfect Nash equilibrium (Nash equilibrium for sequential game). (Hint: count how many nodes each player has.)