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Explain Arrow’s Impossibility Theorem
. Consider the pay-off matrix of a game given below:
|
Player1 | Player 2 | ||
|
| I | O | |
| A | 1,1 | 3,3 | |
| N | 2,4 | 4,2 | |
(a) Find all the Nash equilibrium of this game. Which player(s), if any, would have a dominant strategy?
(b) Suppose that player 1 moves first by choosing either A or N. Players 2 observe player 1’s action and then choose I or, O. For every action combination, the
player’s pay-offs are the same as in the above pay-off matrix. Draw a tree of this new game. How many strategies does player 1 have and what are they? Find all the sub-game perfect equilibria of this game.
What is indirect utility function? How will you derive an indirect utility function from a direct utility function? Explain Roy’s identity?
Explain Arrow’s Impossibility Theorem
Discuss the approaches adopted by Pigou and Pareto for analyzing the problem of
welfare economics
Envelope theorem