Game theory Alex is deciding whether or not to make a loan to Brian who is very poor and who has a bad credit history. Simultaneous to Alex making this decision, Brian must decide whether or not to buy gifts for his grandkids. If he buys gifts, he will be unable to repay the loan. If he does not buy gifts, he will repay the loan. If Alex refuses to give Brian a loan, then Brian will have to go to a loan shark. The payoffs in this game are as follows: if Alex refuses to make a loan to Brian and Brian buys gifts then both Alex and Brian get utility work \$0. If Alex refuses to make a loan to Brian and Brian does not buy gifts, then Alex gets utility worth $0 and Brian gets disutility worth −$1000. If Alex makes a loan to Brian and Brian buys gifts, then Alex gets disutility worth −$2000 and Brian get utility worth $7000. If Alex make a loan to Brian and does not buy gifts, then Alex gets a payoff of utility worth $3000 while that of Brian will be $5000 a) Present the game in normal form and find each individual's dominant strategy and ultimately the Nash equilibrium assuming the game is played once [6 marks] b) With Alex on the first node and Brian on the second node and assuming the game is played ones, present the game in extensive form and identify Nash equilibrium(s) assuming imperfect and perfect information c) Will the Nash equilibrium change if the game is played repeatedly? Explain .