Question

Homework #1 Consider a 3-player setting in which player 1 moves first by choosing among three actions: a, b, and c. After observing the choice of player 1, player 2 chooses among two actions: x and y. 1. Consider the following three variants as to what player 3 can do and what she knows when she moves: If player 1 chose a, then (after player 2 made his choice) player 3 selects among two actions: high and low. Player 3 knows player 2's choice when she moves. Player 3 does not get to move if player 1 chose b or c. Write down the extensive form of this setting. (You can ignore payoffs.) If player 1 chose a, then (after player 2 made his choice) player 3 selects among two actions: high and low. Player 3 does not know player 2's choice when she moves. Player 3 does not get to move if player 1 chose b or c. Write down the extensive form of this setting. (You can ignore payoffs.) If player 1 chose either a or b, then (after player 2 made his choice) player 3 selects among two actions: high and low. Player 3 observes the choice of player 2, but not that of player 1 Player 3 does not get to move if player 1 chose c. Write down the extensive form of this setting. (You can ignore payoffs.) a. b. c.

Answer 1

A_1 = {a, b, c} A_2 = {x, y} A_3 = {H, L} (set of available aitions to the three players)