Question

Three brothers, Huey, Dewey, and Louie, are playing a game. The game uses a 3x3 pegboard. The first player, using the first column, can choose to place his peg in the uppermost row, the middle row, or the bottom row. The next player then chooses what row to place his peg in the middle column. The final player then places his peg in the last column. 7. A player may not choose the same row as the player whose turn was immediately preceding his. Each player scores points by these rules. If the following player's peg is one row away from the preceding player's peg, the preceding If the following players peg is two rows away from the preceding player' peg, the following If the player going third plays the same row as the first player, the first player receives an If a player scores points by two different methods, his total points are the sum of those scores. player scores one point. player scores two points. additional point. The players go in the following order: Huey, Dewey, and Louie. Construct a game tree illustrating the brothers interaction. Find the role back equilibrium (or equilibria). What are the expected payoffs for each player? If a player is indifferent between strategies, assume they will play their choices with equal probability. Show any calculations. (6 pts) a. b.

Answer 1

Round 1 > points table Round 2 > So, the expected payers of each player after Round 3 = 5 points Round 3: - \r\n Round 4: -