A shoplifer and a security guard are playing a simultaneous game. 1. 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
2. If the shoplifter steals and the security guard is not vigilant, she does not get caught and gains 15 and the guard loses 5 .
3. If the shoplifter does not steal and the guard is vigilant, the guard loses 3 for the effort, while the shoplifter gains nothing
4. If the shoplifter does not steal and the guard is not vigilant, neither gain anything.

A simultaneous game was played between a shoplifter and a security guard.

The answer to the game was answered in accordance to the question stated above,

There is no Nash Equilibrium in the game, The shoplifter does not steal in this case, Does not steal, The security guard will be watchful, The security guard ill sleep on the job.

Explanation:

Solution

Given that:

Let our matrix be defined as follows

                                                Security Guard

                              Vigilant or attentive      Not vigilant, less attentive

Shoplifter    Steal           - 20, 15                      15, -5    

              Does not steal  0, 3                          0, 0

Now,

(1) There is no Nash Equilibrium in the game

(2) The shoplifter does not steal in this case

(3) The shoplifter does not steal

(4) The security guard will be watchful

(5) The security guard ill sleep on the job

Note:

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