Chapter 4. Simultaneous Games

6.	For the games in Figures 52, 53, 54 identify which is a coordination game, an outguessing game, and a chicken game. Figure 52 Figure 53 Figure 54
7.	Solve the game in Figure 55 by eliminating the strictly stupid strategies. Figure 55
8.	Assume that you are Player Two in the games in Figures 56, 57, and 58. In each of the games first you make your move, then you have the option of letting Player One see how you move. Finally Player One gets to move. In which of the three games would you want Player One to see how you moved? Figure 56 Figure 57 Figure 58

Answers

6.	Figure 52 is a chicken game, Figure 53 is a coordination game, and Figure 54 is an outguessing game. In Figure 52 the macho strategies are A for Player One and X for Player Two. If one player chooses the macho strategy, and the other, the wimpy strategy, the player who takes the macho course will do much better than his opponent. Figure 53 is a coordination game because the parties want to work with each other to get either A,X or B,Y. The players should be open with each other about their moves. If Player One is going to play A, she wants Player Two to know this so that Player Two will play X. Similarly, if Player One is going to play B, she also wants Player Two to be aware of his move so that Player Two will pick Y rather than X. Figure 54 is an outguessing game because both players want to keep their strategy secret. Thus, Player One would want to keep his move secret and force Player Two to try to outguess him. Player Two would want to adopt a similar outguessing strategy.
7.	A,Y; First eliminate strategy X for Player Two (draw a line through it.) When strategy X is eliminated, you can eliminate strategy B for Player One (draw a line through this), because Player One would only consider playing B if Player Two would play X. Now you can eliminate choice W for Player Two. Finally, you can eliminate strategy C for Player One. This results in Player One picking A and Player Two picking Y.
8.	Figure 56 is a chicken game with B and X as the macho strategies. Player Two would want to play X and then reveal to Player One what she did so it would be in Player One’s interest to play A. In Figure 57 Player One has a dominant strategy of A that he will always play. Thus, it does not matter whether Player One sees Player Two’s move since Player One will always make the same choice. For Figure 58 note that strategy W for Player Two is a strictly stupid strategy and will never be played (draw a line through it). After strategy W is eliminated, strategy A for Player One becomes a strictly stupid strategy, and it too should be eliminated. The resulting game is a coordination game where the players want to play either B and X or play X and Y. As in all coordination games, Player Two wants Player One to know how she is going to move.