Question

Use the following one-shot, normal form game to answer the following questions: Player 2 Left Center Right Up -200, 150 350, 100 -50, 600 Player 1 Middle 200, -300 400, 400 300, 100 What is Player 1's optimal strategy in this game? A) Play "Middle." B) Play "Left." C) Play "Right." D) It depends on Player 2's strategy.

Answer 1

To determine Player 1's optimal strategy in a one-shot normal form game, we look for the maximin strategy by comparing the minimum payoffs for each possible Player 1 strategy. 'Middle' offers the highest minimum payoff, making it the optimal strategy.

Step-by-step explanation:

The subject of the question is game theory, which is a branch of mathematics that deals with the strategic interaction between different players in a situation containing set rules and outcomes. Specifically, this question refers to a one-shot, normal form game where a player needs to determine their optimal strategy.

To find Player 1's optimal strategy, we look at each of the strategies available and compare the payoffs based on Player 2's possible responses. Since Player 1 cannot predict with certainty what Player 2 will choose, Player 1 should consider the strategy that provides the highest minimum gain. This is known as the maximin strategy. If we compare the minimum payoffs of each strategy for Player 1, 'Up' yields a minimum of -200, 'Middle' yields a minimum of 200, and 'Right' yields a minimum of -50. Thus, Player 1's optimal strategy is to play 'Middle' because it guarantees the highest minimum payoff of 200 regardless of Player 2's action.