The following payoff matrix depicts the possible outcomes for two players involved in a game of volleyball.At this point in the game,the ball has just been hit to Deidra,and she chooses whether to hit right or hit left.At the same time,Ashley chooses whether to jump right (Deidra's right)or jump left (Deidra's left).If a player receives a payoff of 1,the player wins the point; if the player receives a payoff of -1,the player loses the point.Use this information to answer the following questions:

-How many Nash equilibrium(s)exist in this game?
A) zero
B) one
C) two
D) three
E) four

Question

The following payoff matrix depicts the possible outcomes for two players involved in a game of volleyball.At this point in the game,the ball has just been hit to Deidra,and she chooses whether to hit right or hit left.At the same time,Ashley chooses whether to jump right (Deidra's right)or jump left (Deidra's left).If a player receives a payoff of 1,the player wins the point; if the player receives a payoff of -1,the player loses the point.Use this information to answer the following questions:
 
-How many Nash equilibrium(s)exist in this game?
A) zero 
B) one 
C) two 
D) three 
E) four

Quizplus · Accepted Answer

In this game, there are no pure strategy Nash equilibria, as each player has a dominant strategy that leads to a better outcome regardless of the other player's choice. Deidra's dominant strategy is to hit to the left, as it leads to a higher payoff (-1 if Ashley jumps left, 0 if Ashley jumps right) regardless of Ashley's choice. Similarly, Ashley's dominant strategy is to jump left, as it also leads to a higher payoff (-1 if Deidra hits right, 0 if Deidra hits left) regardless of Deidra's choice. However, these dominant strategies lead to a (-1,-1) outcome, which is not a Nash equilibrium as neither player has an incentive to switch their choice. Therefore, the game has no Nash equilibria.

The Following Payoff Matrix Depicts the Possible Outcomes for Two