The following payoff matrix depicts the possible outcomes for two players involved in a game of Rock,Paper,Scissors.If a player receives a payoff of 1,the player wins; if the player receives a payoff of -1,the player loses; if both players receive 0 (zero),the players tie.Which of the following statements is true?

A) Will's dominant strategy is to play rock,and Grace's dominant strategy is to play rock.
B) Will's dominant strategy is to play paper,and Grace's dominant strategy is to play rock.
C) Will's dominant strategy is to play rock,and Grace's dominant strategy is to play paper.
D) Will's dominant strategy is to play scissors,and Grace does not have a dominant strategy.
E) Neither Will nor Grace has a dominant strategy.

Question

The following payoff matrix depicts the possible outcomes for two players involved in a game of Rock,Paper,Scissors.If a player receives a payoff of 1,the player wins; if the player receives a payoff of -1,the player loses; if both players receive 0 (zero),the players tie.Which of the following statements is true?
   
A) Will's dominant strategy is to play rock,and Grace's dominant strategy is to play rock. 
B) Will's dominant strategy is to play paper,and Grace's dominant strategy is to play rock. 
C) Will's dominant strategy is to play rock,and Grace's dominant strategy is to play paper. 
D) Will's dominant strategy is to play scissors,and Grace does not have a dominant strategy. 
E) Neither Will nor Grace has a dominant strategy.

Quizplus · Accepted Answer

A dominant strategy is one that yields the highest payoff for a player regardless of the strategy adopted by the other player. In this game, neither Will nor Grace has a dominant strategy because the optimal strategy depends on the other player's choice. For example, if Will chooses rock, Grace's optimal strategy is to play paper; if Will chooses paper, Grace's optimal strategy is to play scissors, and so on. Therefore, the best choice is E, as neither player has a dominant strategy in this game.

The Following Payoff Matrix Depicts the Possible Outcomes for Two