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Game Theory Assignment - Nash Equilibrium

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Added on  2020-02-24

Game Theory Assignment - Nash Equilibrium

   Added on 2020-02-24

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Running head: GAME THEORY Game TheoryName of the StudentName of the UniversityAuthor Note
Game Theory Assignment - Nash Equilibrium_1
1GAME THEORYTable of ContentsAnswer 1:.........................................................................................................................................2Answer 2a:.......................................................................................................................................3Answer 2b:.......................................................................................................................................6Answer 3:.........................................................................................................................................7References......................................................................................................................................11
Game Theory Assignment - Nash Equilibrium_2
2GAME THEORYAnswer 1: In the given two person game, Strategy ABCPlayers 1 D9,67,68,7E8,106,89,9F7,85,87,10There is no pure Nash equilibrium. A Nash equilibrium, in a two-person game occurs at apoint where, both the persons have their welfare maximized and from where none of them hasthe incentive to deviate. That means, at the Nash Equilibrium, both the players are choosing theiroptimal strategies and there is no better combination of strategies for the players, given theconditions (Myerson 2013). Here, there is no such single point where, both the players are maximizing their profit.This implies, there is no pure Nash Equilibrium in this game. Here, if 1 chooses D, 2 chooses C, but if 2 chooses C, 1 chooses E. If 1 chooses E, 2 chooses A, but if 2 chooses A, 1 chooses D. If 1 chooses F, 2 chooses C, but if 2 chooses C, 1 chooses E. Therefore, there is no Nash equilibrium in the above game (Colman 2016). In this game, Player 1 will never choose strategy F, as it is a dominated strategy, that means theprobability of playing F is 0: Let, x be the probability of Player 1 playing D and y be the probability of Player 1 playing E.
Game Theory Assignment - Nash Equilibrium_3
3GAME THEORYTherefore, 9.x +8.y = 7.x +6.y This means, x = y Again, x + y + 0 = 1 This means, x = y = 0.5 This means the expected pay off of A is = (9*0.5) + (8*0.5) = 4.5 +4 = 8.5 (Dixit and Skeath2015. Player 2 will never play strategy B as it is a dominated strategy, this means the probability is 0. Let p be the probability of 2 playing A and q be the probability of 2 playing C: Therefore, 6.p + 7.q = 10.p + 9.q 4.p = -2.q , which implies p/q = -1/2. However, probabilities cannot be negative, which impliesthe expected payoff of Player 2 is unidentified. Answer 2a: In this problem, both the firms are assumed to be rational and there are perfectinformation by both the firms. Therefore, the output of one firm is dependent on the strategy ofother firm and the optimal outputs can be calculated from the reaction functions of both thefirms. Here, the revenue of Firm 1 is: R1 = P*X1 = [1000 – X1 – X2]*X1
Game Theory Assignment - Nash Equilibrium_4

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