Four friends want to play basketball this afternoon. They all are very busy during the day...

 

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Four friends want to play basketball this afternoon. They all are very busy during the day and don't have time to communicate whether they will go to the basketball court (strategy P) or not (strategy N). A match can only be played with exactly two or four players. If the match can be played, each of the four friends gets a benefit of 5 (even those who don't participate). Every friend who goes to the court bears a cost of 3 (regardless of whether the match is played or not). A friend who doesn't participate bears a cost of 1. Hence, the payoff of a friend who chooses P is 2 if the match is played, and -3 if the match is not played, while the payoff of a friend who chooses N is 4 if the match is played, and -1 otherwise. (a) (2 points) How many pure strategy profiles does this game have? (b) (2 points) What is the best response of a friend to every possible combination of strategies for the other three friends? (c) (4 points) Find all pure-strategy Nash equilibria of this game. How many pure- strategy Nash equilibria are in this game? (d) (2 points) Compute a symmetric mixed-strategy Nash equilibrium in this game in which every friend goes to the court with the same probability p = (0,1). (It is ok if you cannot solve for the exact p, as long as you can write the correct equation from which you would compute the exact p.) Four friends want to play basketball this afternoon. They all are very busy during the day and don't have time to communicate whether they will go to the basketball court (strategy P) or not (strategy N). A match can only be played with exactly two or four players. If the match can be played, each of the four friends gets a benefit of 5 (even those who don't participate). Every friend who goes to the court bears a cost of 3 (regardless of whether the match is played or not). A friend who doesn't participate bears a cost of 1. Hence, the payoff of a friend who chooses P is 2 if the match is played, and -3 if the match is not played, while the payoff of a friend who chooses N is 4 if the match is played, and -1 otherwise. (a) (2 points) How many pure strategy profiles does this game have? (b) (2 points) What is the best response of a friend to every possible combination of strategies for the other three friends? (c) (4 points) Find all pure-strategy Nash equilibria of this game. How many pure- strategy Nash equilibria are in this game? (d) (2 points) Compute a symmetric mixed-strategy Nash equilibrium in this game in which every friend goes to the court with the same probability p = (0,1). (It is ok if you cannot solve for the exact p, as long as you can write the correct equation from which you would compute the exact p.)

Answer rating: 100% (QA)

In a tennis game scenario with four friends there are 16 pure strategy profiles Two purestrategy Nash equilibria exist and a symmetric mixedstrategy N... View the full answer