Consider the following coordination game, where the payoffs are in dollars. Player 2 R Player 1...
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Consider the following coordination game, where the payoffs are in dollars. Player 2 R Player 1 U 4, 1 0,0 D 0,0 1,4 (a) Find any Nash cquilibria for this coordination game. (b) Suppose that before the game is played, there is an initial stage where player 1 chooses whether or not to burn $2. Player 2 knows that Player 1 has this option and Player 2 observes Player l's action. Then the players play the coordination game shown above. Since player 2 knows that player 1 has the option to burn the money, this "moncy burning" could be viewed as a way that Player 1 communicates their intention to Player 2. Draw an extensive form game that includes both stages of this new game: stage 1, where Player 1 chooses whether or not to burn $2, and stage 2, when the players play the coordination game. Note that whenever Player 1 burns $2, this decreases their own payoff by $2 (this should be reflected in the payoffs of the extensive form game). (c) Write out the normal form game for the 2-stage extensive form game and identify any Nash equilibria. I usually do not ask you to draw out very large normal form games - this is a bit of an exception - you should arrive at a normal form game where 1 player has 8 strategies and the other has 4. (d) Use iterative climination of weakly dominated strategies to reduce the game. There is a way to reduce this (over multiple iterations) to a game where player 1 has 2 remaining strategics and player 2 has 1 remaining strategy. (e) Based on your result in the previous part, summarize the way Player l's option to burn money affects the outcome of this two stage game (compared with the coordination game without money burning). Consider the following coordination game, where the payoffs are in dollars. Player 2 R Player 1 U 4, 1 0,0 D 0,0 1,4 (a) Find any Nash cquilibria for this coordination game. (b) Suppose that before the game is played, there is an initial stage where player 1 chooses whether or not to burn $2. Player 2 knows that Player 1 has this option and Player 2 observes Player l's action. Then the players play the coordination game shown above. Since player 2 knows that player 1 has the option to burn the money, this "moncy burning" could be viewed as a way that Player 1 communicates their intention to Player 2. Draw an extensive form game that includes both stages of this new game: stage 1, where Player 1 chooses whether or not to burn $2, and stage 2, when the players play the coordination game. Note that whenever Player 1 burns $2, this decreases their own payoff by $2 (this should be reflected in the payoffs of the extensive form game). (c) Write out the normal form game for the 2-stage extensive form game and identify any Nash equilibria. I usually do not ask you to draw out very large normal form games - this is a bit of an exception - you should arrive at a normal form game where 1 player has 8 strategies and the other has 4. (d) Use iterative climination of weakly dominated strategies to reduce the game. There is a way to reduce this (over multiple iterations) to a game where player 1 has 2 remaining strategics and player 2 has 1 remaining strategy. (e) Based on your result in the previous part, summarize the way Player l's option to burn money affects the outcome of this two stage game (compared with the coordination game without money burning).
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a There are two nash equilibrium in this game ie UL and DR Given that player 2 plays L it is best to ... View the full answer
Related Book For
Intermediate Microeconomics and Its Application
ISBN: 978-0324599107
11th edition
Authors: walter nicholson, christopher snyder
Posted Date:
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