If Player 2 thinks that Player 1 will play Down, what move will he do ? Left or Right ?

Which of the following assertions is true :

What is the formula for  ?

Is there a pure Nash Equilibrium in this game ? If you think so, you choose the answer with the good strategy below (strategy player 1, strategy player 2). If not, you just answer No Pure Nash Equilibrium.

In fact, the bank decides to keep the 177 000 values above 1000 € to decide the threshold of alert. These 177 000 are put in a variable named . These data are fit with a generalized Pareto Distribution with the following parameters:

.

Looking at the documentation of the software, the distribution function of this Generalized Pareto Distribution has the following formula: 

.

What is the formula that allows you to compute the VaR of the variable  at the threshold  ?

In the course, we have seen a graphical method to choose a threshold. What is the name of this method ?

The software that you use to fit the parameters of the distribution function  of , uses the following formulas for the GEV, depending of the parameters   :

 if : 

,

if  :

.

What is the formula giving the VaR at  of the random variable  with respect to the parameters  . Use the good formula depending on the value of .

What is the most important property of a Nash Equilibrium ?

According to you, the law obtained after adjusting the law of in the previous question (i.e. for the function  ) is. 

The bank decides to take  for the VaR of the  variable (i.e. the 177 000 transactions above 1000 €). What is the value of threshold of alert ? (You don't need to write the cents. A tolerance of 5€ is admitted. You write an integer number, without any other symbol.