Part 4 (11 marks) Pingping (Player 1), Anan (Player 2) and Dandan (Player 3) play a game. Each player is given an unmarked envelope and asked to put in it either nothing or 3 yuan of her own money or 6 yuan of her own money. A teacher collects the envelopes, opens them, gathers all the money and then doubles the amount (using her own money) and divides the total into three equal parts which she then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts 6 yuan, then the teacher adds another 6 yuan so that the total becomes 12 yuan, divides this sum into three equal parts and gives 4 yuan to each player. Each player is selfish and greedy, in the sense that she ranks the outcomes exclusively in terms of her net change in wealth (what she gets from the teacher minus what she contributed). a. Represent this game by means of a set of tables. (Note: do not treat the teacher as a player.) (6 marks) b. For Pingping and each pair of strategies, does she have a dominant strategy? If she has, what is her dominant strategy? (2 marks) c. Suppose three players meet in person to coordinate the money, and Dandan promises to put 6 yuan. Is this promise credible? What would be the likely outcome