One Step Ahead of Best Responses
Game theory involves analyzing the possible strategies that are available to not only you, but also all the other participants, and weighing the possible payoffs that can come from your choices. However, in some games, it isn’t enough to just know what the best strategy is; you also have to figure out what your best strategy is now that everyone else knows what the best strategy is. To put it simply, there are some instances where the winning strategy isn’t to pick the best response, but instead pick based on what you think everyone else will pick. For example, the best response for travelling from A to B might be the bridge that connects the two towns. However, everyone else knows that that bridge is the best response, and it might actually take you longer to go across the bridge because of traffic congestion rather than taking the longer road and going around.
The economic world works in a similar fashion. Investing in the stock market isn’t necessarily always trying to pick the best response; it involves picking the option that other people think is the best response. Many companies produce products that are tailored to what they believe the general public think is the best response. The minority game, which involves choosing between two choices, has the player trying to pick the option with less votes, or what they believe is the choice that other participants don’t think is the best response.
However, if you can think ahead, then others can as well, which means that you have to think even further ahead. There was an experiment where you had to guess what 2/3 of the national average was on a scale between 0 and 100. If you thought the average was 63, then your answer is 42. If you thought the average was 9, then our answer is 6, and so on. The actual answer ends up being somewhere around 20. Most people know that the average will be 50, so the best response is around 33. However, since most people know that most people know that the best response is 33, they go a step further and predict that the answer is around 20. If this continues on, the all the answers should be around 0, which is the Nash Equilibrium of this experiment. However, human beings generally only have the capability to think around 1-3 steps ahead because people think that they’re outsmarting everyone else and are one step ahead of the general population. This phenomenon is called “k-step thinking”.
Link: http://www.nytimes.com/interactive/2015/08/13/upshot/are-you-smarter-than-other-new-york-times-readers.html