A New Form of Games–Summer

Today, I’m going to introduce you to a new form of game different from all the games I’ve mentioned in my previous posts! Today, we are going to play a sequential game!

What is a sequential game? How is it different?

In our previous games, all the players make their decisions simultaneously without knowing each other’s decision. Yet, in today’s game, one of the player is going to make the decision first and the other player will make his/her decision knowing the first person’s choice. We call these games with a sequence of moves a sequential game (for additional information and examples of sequential game, check this out!). One of the most famous sequential games in reality is taking out a loan.

Let’s assume that a Westtown student wants to establish a startup business like Shike Coffee and needs to take out a loan from the bank for initial funding. The bank has two choices for the size of the loan: give him/her a small amount of loan (\$1000), or give him/her a large amount of loan (\$3000). The student then has the choice of whether to use the loan money wisely or to squander it. If s/he invest the \$1000 wisely, s/he will earn a profit of \$1500 after paying back the loan. If s/he invest the \$3000 wisely, s/he will earn a profit of \$2000 after paying back the loan. In these cases, the bank will profit \$1000 and \$3000 respectively from the loan. On the other hand, the student can waste the loan (profiting \$1000 and \$3000 respectively) and the bank will gain nothing.

In the case of a sequential game, it would be more appropriate to represent the situation with a decision tree:

Since the student’s strategies depend on the bank’s decision, let’s consider the most logical strategy for the bank. When the bank makes the decision, it needs to keep in mind the student’s best response in each situation. The bank uses a method called backward induction, which is reasoning backwards from the end of the problem to determine the best sequence of action.

In the second step, if the bank loans the student \$1,000, the student will work hard and pay it back because then s/he can have a profit of \$1,500 instead of only \$1,000. Yet, if the bank loans the student \$3,000, the student will not have incentive to work hard because s/he will have \$3000 of profit from not pay back the loan instead of \$2,000. Thus, the bank knows that the student will not work hard if s/he receive a huge loan. As a result, the bank tends to give the student a small loan of \$1,000 instead of \$3,000.

According to game theory, banks are more likely to give out small loans spread out in a period of time. Yet, for many startup companies, the very beginning requires a lot of financial investments that cannot be covered by a small loan. Thus, in order that the bank is more reassured that the loan would be paid back, it establishes restrictions for the loaner such as credit monitoring system, laws, spending restrictions, mortgage etc.

Sequential games are prevalent in many areas in our real life including but not limited to loans, health insurance, chess, and wars. In the following posts, I would continue to explore with you concepts within sequential games through real life examples.

See you next week!