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# Game Theory

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Homer and Marge are playing the attached simultaneous-move, one-shot game.

(a) Does either player have a strictly dominant strategy?
(b) What is the solution to this game? Is the solution a Nash equilibrium?
(c) Suppose that this simultaneous-move game is modeled as a sequential-move game with Homer moving first. Illustrate the extensive form of this game.
(d) Use backward induction to find the subgame perfect equilibrium.
(e) Suppose that Marge moves first. Illustrate the extensive form of this game and use backward induction to find the subgame perfect equilibrium.

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The expert examines game theory simultaneous-moves and one-shot games.

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Question 1.
Part a) There are three strategies Bart, Lisa and Magie. A dominant strategy is the one which will give the player maximum outcome, irrespective of the choice of the opponent. To identify a dominant strategy, follows these steps:
1. To identify whether there is a dominant strategy for Marge or not, look at the table row wise.
2. The first row gives the payoffs, when Homer chooses bart strategy. In the cell first amount represent pay off to Homer and second pay off to Marge. In the first row look at the second payoffs i.e. pay offs to Marge
3. The pay offs to Marge are 150, 250 and 350 for the three strategies. Since 350 is the highest payoff, Marge will naturally choose Maggie strategy.
4. Look at the second row, this represent the payoffs when Homer choose Lisa strategy, the payoffs to Marge are 125, 150 and 245 for three strategies. Again he will chose Maggie as the payoffs are maximum for this strategy at 245.
5. Look at the last row, the payoff to Marge are 250, 275 and 300. Again Marge will chose Maggie strategy as it gives the highest pay off at 300.
6. Thus for all the strategies of Homer, Marge has the best strategy as Maggies. So this is the strictly dominant strategy chosen irrespective of the choice of ...

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