Question

Consider the following game. Player 1 moves first and can choose A or B. If Player 1 chooses A, then Player 2 then moves and can choose C or D. The payoffs for P1 and P2 are as follows: AC = (4, 2), AD = (2,3). If Player 1 chooses B the payoffs for P1 and P2 are (1, 5). Using backwards induction, solve for what each player will choose and what the player's payoff in the game will be. This question is worth 6 points and there are 2 correct answers. You should select ALL 2 answers if you know them but you can select only 1 answer if you are not sure of ALL of the correct answers. You receive 3 points for each correct answer but lose 3 points for an incorrect answer. You should choose ALL 2 of the correct answers if you know them but it is probably not a good idea to guess at an answer unless you are pretty sure. For example, if you select 1 correct answers and 1 incorrect answer you would receive 3-3 = 0 points for the question. You cannot receive less than 0 points on the question; for example if you select 2 incorrect answers you would receive 0-6-0 points for the question. A little game theory for the game theory questions. Choose ALL of the correct answers. 3 points for a correct answer, -3 points for an incorrect answer.

A. Player 1 will choose A
B. Player 1 will choose B
C. Player 2 will choose
D. C Player 2 will choose
E. D Player 2 will not get a choice

Answer 1

Player 1: A (Payoff: 4)

Player 2: C (Payoff: 2)

The players' optimal strategy, reached through backward induction, is for Player 1 to choose A and Player 2 to choose C, resulting in payoffs of 4 and 2, respectively.

Step-by-step explanation:

In this sequential-move game, we employ backward induction to determine the optimal strategies and payoffs for both players. Starting at the last move, Player 2 must decide between choosing C or D. Comparing the payoffs, (4, 2) for C and (2, 3) for D, Player 2 will choose C as it yields a higher payoff. Now, with knowledge of Player 2's rational choice, Player 1 evaluates their options. If Player 1 chooses A, the payoff is (4, 2), which is superior to the payoff of (1, 5) if Player 1 chooses B. Hence, Player 1 will choose A as it leads to a higher payoff.

The optimal strategy is for Player 1 to choose A and Player 2 to choose C. The resulting payoffs are 4 for Player 1 and 2 for Player 2. This solution is consistent with the principles of backward induction, where each player maximizes their payoff given the anticipated optimal response of the other player.