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:

http://oyc.yale.edu/economics/econ-159#overview

http://mindyourdecisions.com/blog/category/game-theory/

Images:

http://adgears.com/wp-content/uploads/2015/11/two-quarters.jpg

MaxI like the way you used a coin game to demonstrate an otherwise hard-to-explain concept. Just curious, though, if the case was really to be played out, what would you choose? In your case of “you and your friend”, does your knowledge about your friend’s personality affect the choice? Are there any assumptions you have to make while playing the game? If so, what are they?

tkbarnetPost authorFor this example I just assumed that there was no collusion between the players. If I had a chance to talk with my friend during the coin game, the best choice would for me to pick tails and him to pick heads, and then we could just split the four tickets between us.

kevinwang11Tom, very intriguing illustration of the “importance of another person’s shoes.” The “coin game” effectively conveys your point that a person’s own outcome can be influenced by another person. I could not agree more with your statement that recognizing what others are thinking is not only key to games but also to many real world situations.

A question for you: On what occasion would a “strictly dominated strategy” be applied?

Max D.I think it would be better for Tom to illustrate the difference between a dominated strategy and a dominant strategy first, then answer your question. Having done some work in game theory, I feel that it would be very confusing for others if only the dominated or the dominant is discussed, without the mentioning of the counterpart.

tkbarnetPost authorKevin, are you asking when a strictly dominated strategy should be chosen or when a strategy is strictly dominated?

kevinwang11When should a strictly dominated strategy should be chosen?

tkbarnetPost authorA strictly dominated strategy has by definition another strategy that always has a higher payoff that itself, no matter what others do. And if that is the case, there is no reason to ever pick the strictly dominated strategy, as the outcomes would be greater if you choose the dominating strategy. However in Max’s case, if there was cooperation that would change the payoffs, and it would no longer be a dominated strategy.

dexcoengilbertI really liked the simplicity of the example you used Tom. It made me relive some fun memories of a week of these games in Econ last year. It would be really nice if you put up one of the 2×2 boards on a post so we see all the payoffs in a clear box.

tkbarnetPost authorThat’s good advice, I’ll start using those next week.