Question

A thief and a security guard are playing a simultaneous game. The thief will choose whether or not to steal, while the guard will choose whether or not to be vigilant. If the thief steals and the security guard is vigilant, the thief gets caught and suffers a loss of 20, while the security guard gets a bonus worth 15. However, if the thief steals and the security guard is not vigilant, the thief does not get caught and gains 15, while the guard loses 5. On the other hand, if the thief does not steal and the guard is vigilant, the guard loses 3 for the effort, while the thief gains nothing. Finally, if the thief does not steal and the guard is not vigilant, neither one of them gain anything. ​What is the Nash equilibrium of this simultaneous game? ​Steal, Vigilant ​Steal, Not vigilant ​Not steal, Vigilant ​The game has no Nash equilibrium

Answer 1

guard/thief	Steal	Not Steal
Vigilant	15,-20	-3,0
not vigilant and not caught the thief	-5,15	0,0

given above is the matrix form of the given game . Here if the guard is vigilant is given ,. it is best for the thief to not steal . Similarly, if the guard ois not vigilant , it is best for the thief to steal because he would not get caught and hence has a higher payoff there.

On the other hand if the thief decides to steal the best strategy for guard is to be vigilant and if he decides to not steal, the guard decides to ne not vigilant since in that case he gets a higher payoff and does not lose his effort.

so there is no nash equilibrium in this case.

Answer is option D)No nash equilibrium

(You can comment for doubts )