Appendix: Study Questions

It signifies nothing to play well if you lose.

Proverb¹

Chapter 2. Threats, Promises, and Sequential Games

1.	What is the likely outcome to the game in Figure 47? Figure 47
2.	What is the likely outcome to the centipede game in Figure 48? Figure 48
3.	In the games in Figures 49, 50, and 51, Player Two threatens to be mean to Player One if Player One is first mean to Player Two. In which games is Player Two’s threat to retaliate credible? Figure 49 Figure 50 Figure 51
4.	Yesterday you bought a movie ticket for $8. When you arrive at the theater today you realize the ticket is lost. Should you buy another ticket?2

Answers

1.	Player One picks A, and Player Two chooses U. This outcome gives each player a payoff of 20. Player One will not choose C because if he did, Player Two would maximize her payoff by picking Z, which would give Player One a payoff of zero. Player Two would like to be able to credibly promise Player One that if Player One picks C, she will pick Y. Such a promise, however, lacks credibility because given that Player One picks C, Player Two gets a higher payoff by choosing Z over Y.
2.	Player One should immediately move down ending the game. If the game were to reach the final node, Player Two would move down to get a payoff of 4, rather than move across and get only 3. Consequently, at the second to last node Player One should move down to get 3 rather than move across and get only 2 when Player Two moves down. You can similarly show that each player is always better off moving down than across. This outcome seems very wasteful because had the parties worked together and made it to the last node, they both would have done much better. Unfortunately, as in much of game theory, rational mistrust dooms the players to low payoffs.
3.	This threat is credible only in Figures 49 and 50. Player Two’s threat to be mean is only credible if (given that Player One is mean) Player Two is better off being mean than nice.
4.	You should buy another ticket. The lost $8 is an irrelevant sunk cost that you should ignore. Unless you have acquired new information about the movie, if it was worth $8 yesterday to attend it should still be worth $8 today.