1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game in our online class? Explain your reasoning.

2.) Continue to consider this discrete Bertrand model, but now assume that each student has a constant cost of 5 that is deducted from allpayoffs. So, whoever has the low number wins their number, minus 5. Whoever has the high number loses 5total. In the event of a tie, each student wins an amount equal to their number divided by two, then minus five. Find any Nash equilibria in this game. Explain your reasoning.Hint: It is perfectly fine for both players to have losses in equilibrium!There are more than 1 Nash equilibria.