Problem
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 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).
1. Represent this game by means of a set of tables. (Hints: Note that we can represent a three player game with a set of tables: Player 1 chooses the row, Player 2 chooses the column and Player 3 chooses the table (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)).
2. Find the Nash equilibria of the above game.