There are three players. Each player is given an unmarked envelope and asked to put in it either nothing or 3 of his own money or 6 of his own money. A referee collects the envelopes, opens them, gathers all the money and then doubles the amount (using his own money) and divides the total into three equal parts which he then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts 2 6, then the referee adds another 6 so that the total becomes 12, divides this sum into three equal parts and gives 4 to each player. Each player is selfish and greedy, in the sense that he ranks the outcomes exclusively in terms of his net change in wealth (what he gets from the referee minus what he contributed). (a) Describe this game by means of a set of matrices. (Hints: Note that we can represent a three player game with a set of matrices: Player 1 chooses the row, Player 2 chooses the column and Player 3 chooses the matrix (that is, we label the rows with Player 1's strategies, the columns with Player 2's strategies and the tables with Player 3's strategies)). (b) Find the Nash equilibria of the above game.
There are three players. Each player is given an unmarked envelope and asked to put in it either nothing or 3 of his own money or 6 of his own money. A referee collects the envelopes, opens them, gathers all the money and then doubles the amount (using his own money) and divides the total into three equal parts which he then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts 2 6, then the referee adds another 6 so that the total becomes 12, divides this sum into three equal parts and gives 4 to each player. Each player is selfish and greedy, in the sense that he ranks the outcomes exclusively in terms of his net change in wealth (what he gets from the referee minus what he contributed). (a) Describe this game by means of a set of matrices. (Hints: Note that we can represent a three player game with a set of matrices: Player 1 chooses the row, Player 2 chooses the column and Player 3 chooses the matrix (that is, we label the rows with Player 1's strategies, the columns with Player 2's strategies and the tables with Player 3's strategies)). (b) Find the Nash equilibria of the above game.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:There are three players. Each player is given an unmarked
envelope and asked to put in it either nothing or 3 of his own money or 6 of his own money.
A referee collects the envelopes, opens them, gathers all the money and then doubles the
amount (using his own money) and divides the total into three equal parts which he then
distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts
2
6, then the referee adds another 6 so that the total becomes 12, divides this sum into three
equal parts and gives 4 to each player. Each player is selfish and greedy, in the sense that
he ranks the outcomes exclusively in terms of his net change in wealth (what he gets from
the referee minus what he contributed).
(a) Describe this game by means of a set of matrices. (Hints: Note that we can represent
a three player game with a set of matrices: Player 1 chooses the row, Player 2 chooses
the column and Player 3 chooses the matrix (that is, we label the rows with Player
1's strategies, the columns with Player 2's strategies and the tables with Player 3's
strategies)).
(b) Find the Nash equilibria of the above game.
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