The lesson I want to discuss this week once again concerns the importance of interacting with others in the application of game theory. And, if you remember how I defined a game, (any strategic situation when one person’s actions affects another’s), the importance of the other person is clear. You are not able to make the best decision if you ignore the information about the other player. Last week I talked about what you knowing what each person wants, also known as their payoffs. This week I am going to go a step farther, and I am going to discuss the importance of knowing what the other person is thinking.
When considering how the other player is going to act, it is useful to first check if there are any strictly dominated strategies. Two things to quickly clarify here is the terms strategy and a strictly dominated strategy. A strategy is any action that a player can take, pretty simple. A strictly dominated strategy is a strategy that will always have a lower payoff than another strategy, no matter what others do. This is useful since any rational player will never pick a strictly dominated strategy, because they would always get a better outcome if they chose the dominating strategy.
Let me give you an example to further your understanding. Say you and a friend went up to a table at a carnival and you are each handed a coin. You are each told to choose one side of the coin, either heads or tails. If you friend picks heads he will get one ticket, and if he picks tails, he will get two tickets. Now your side is a bit more complicated. If you pick heads, you will always get one ticket. However, if you pick tails and your friend picks heads you will get three tickets, but if you both pick tails you will get no tickets.
Now if your friend was random and just flipped the coin, there would be a logical argument to choose tails. The average outcome of tails, given a fifty fifty coin, is one half, just a bit more than the average outcome of one that heads has. However people aren’t random, they act to fulfill their own interests, in this case getting tickets. Your friend would logically see that heads is a strictly dominated decision, since he would always get more tickets choosing tails. Knowing this, you should never pick tails, as then you would get no tickets. Instead, after stepping into your friends shoes, it becomes clear that the best decision is heads.
This doesn’t just apply to trivial carnival games, but any interdependent situation where the action of another person affects your own possible outcomes. If you can reason out what the other player is going to choose, then it helps to let that inform your own decision. Putting your self in another person’s shoes will get you closer to the best outcome possible.
I hope you learned something this week, and thanks for reading.
For anyone who wants to follow their own interest in game theory, here are a few resources: