Question Three: Game Theory and Financial Markets [42 marks] a) What is game theory? [3 marks] For each of the following strategic form of games, mention if there is a strictly or weakly dominant strategy [1 mark each] and in each case write down the Nash Equilibrium of the game [2 marks each). b b) b b 1,1 0,0 b 0,0 0,0 c) a a 2,2 0.0 b 0,0 1,1 b d) a a b b 50,50 90,10 b 80,20 20,80 e) a a b a 0,0 -1,3 b 3,-1 1,1 You are a loans officer at a local bank. You have a total of R5 million (m) that you can issue as a loan to potential clients. If you decide not to issue a loan to any client, you obviously will not have any payoffs attached to the R5m. If you loan out R2m, the payoff will be a net interest of Rim for the bank and Rim for the client, if the client does not run away with the R2m. If you issue R5m, the payoff will be a net interest of R2m for the bank and R3m for the client, if the client does not run away with the R5m. f) Use the sequential form of a game (and clearly show its tree in your answer) to make a decision on how much you would issue as a loan. [7 marks] g) Use the strategic form of a game (and clearly show its table in your answer) to make a decision on how much you would issue as a loan. [7 marks] h) There are two sub-games in this loan scenario. What are the sub-game perfect equilibria in these games? [6 marks] Are these sub-game perfect equilibria informative enough to assist you to make a decision? [one mark for a yes or no] Why? [2 marks] Now assume that your bank can take the client to court in the event that the client runs away with the amount given to him/her. The bank will face costs of-c if it takes the client to court, and the client will be forced by the court to repay the amount that she took. i) Use the sequential form of a game (and clearly show its tree in your answer) to now let us know if this new information changes your initial decision taken in (f) above. [6 marks] j) What are the sub-game perfect equilibria based on this new information? [2 marks] k) Provide a commitment strategy that you can come up with to restrict the client from running away after receiving a loan. [2 marks]