Consider the 3 x 3 game below where the first number in each cell shows the money payoff for the Row player and the second number in each cell shows the money payoff for the Column player. L C R U 5, 5 0, 4 8, 4 M 4, 6 11, 2 0, 0 D 4, 2 10, 10 2, 11 (a) On the assumption that each player is risk neutral and cares only about his/her own payoff, and on the further assumption that a Level-0 player picks a strategy entirely at random, this game distinguishes between three 'types' of players, namely Level-1, Level-2 and Nash. What would Level-1 Row and Column players each choose? What strategies would be chosen by Level-2 Row and Column players? What are the Nash Equilibrium. strategies for each player? In all cases, explain how you arrived at your answers. [8 marks] (b) How do things change if we replace the assumption that each player cares only about his/her own payoff by the assumption that each player is inequality averse to the extent that he/she would rather both players receive a payoff of 10 than that he/she receives 11 while the other player receives 2? [6 marks] Next, consider the following two 2 x 2 games where the first number in each cell shows the money payoff for the Row player and the second number in each cell shows the money payoff for the Column player. Game 1 Game 2 L R L R U 4, 0 0, 1 U 9, 0 0, 1 D 0, 1 1, 0 D 0, 1 10 (c) Are there any Nash equilibria in pure strategies in either game? If so, identify it/them. Otherwise, explain why there is not. [2 marks] (d) Whether or not there are any pure-strategy Nash equilibria, there is a Mixed Strategy Nash Equilibrium (MSNE) in each game. Compute the MSNE for each game, showing how you arrived at your answers. [6 marks] (e) Describe how Ochs (1995) used those games to test the descriptive power of MSNE. He concluded that Quantal Response Equilibrium (QRE) did a better job of fitting the data. Summarise how QRE works and how it provides a better fit. [11 marks] END OF THE P