Use the following case from question
A shoplifter and a security guard are playing a simultaneous game.If the shoplifter steals and the security guard is vigilant,the shoplifter gets caught she suffers a loss of 20,and the security guard gets a bonus worth 15.If the shoplifter steals and the security guard is not vigilant,she does not get caught and gains 15 and the guard loses 5.If the shoplifter does not steal and the guard is vigilant,the guard loses 3 for the effort,while the shoplifter gains nothing and if the shoplifter does not steal and the guard is not vigilant,neither gain anything
-What is the Nash equilibrium of this simultaneous game?
A)Steal,Vigilant
B)Steal,Not vigilant
C)Not steal,Vigilant
D)The game has no Nash equilibrium

Question

​Use the following case from question
A shoplifter and a security guard are playing a simultaneous game.If the shoplifter steals and the security guard is vigilant,the shoplifter gets caught she suffers a loss of 20,and the security guard gets a bonus worth 15.If the shoplifter steals and the security guard is not vigilant,she does not get caught and gains 15 and the guard loses 5.If the shoplifter does not steal and the guard is vigilant,the guard loses 3 for the effort,while the shoplifter gains nothing and if the shoplifter does not steal and the guard is not vigilant,neither gain anything
-​What is the Nash equilibrium of this simultaneous game?
A)​Steal,Vigilant
B)Steal,Not vigilant
C)Not steal,Vigilant
D)​The game has no Nash equilibrium

Quizplus · Accepted Answer

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Here, no single strategy pair meets the criteria for a Nash equilibrium. If the shoplifter decides to steal, the guard's best response is to be vigilant, but then the shoplifter's best response would be not to steal, which in turn would make the guard's best response to not be vigilant. This cycle indicates that there is no stable strategy pair where both players' strategies are best responses to each other, leading to the conclusion that the game has no Nash equilibrium.

​Use the Following Case from Question

Use the Following Case from Question