Game Theory

When deciding on an action, we often must consider how the actions chosen by others impact what is best for us. Think of a pitcher in baseball. Is it better to throw a fastball or a change up? Well, it depends. If the batter is expecting fastball, then a change up would be ideal. But if the batter is sitting back anticipating a change up, best to throw the fastball. So in a nutshell, what is best for the pitcher ultimately depends on the actions of the batter.

If I try to list examples of scenarios like the one above, where the best actions for one individual depend on the choices of others, they come rather easily:

  • the decision of whether it is better to serve to the forehand or the backhand in tennis depends on whether the opponent is prepared for one more than the other;
  • in tic-tac-toe (similar for checkers or chess), playing any move (say, an X in the top-left corner) may or may not be optimal, depending on the prior moves taken by your opponent;
  • in the game of rock-paper-scissors, no one move is always best – the best strategy depends precisely on what your opponent plays.

There are even more examples of these kinds of interactions in economic applications:

  • a decision to take a highly risky action may depend on the likelihood of a bail out if the risk does not pay off (thinking of teenagers being bailed out by their parents, or banks/business being bailed out by the government);
  • in many industries, the optimal price to charge may vary, depending on how much competitors are charging;
  • the best locational choice for a business (bank, gas station, car dealership) likely depends on where other similar establishments locate.

What about other important social or political applications?

  • A political candidate may choose a position or platform on an issue differently based on the stance of his opponent in the election;
  • an attacking military may target different locations, based on the enemy’s allocation of defensive forces;
  • a criminal may choose to commit or not commit a crime, depending on factors such as the level of security and the presence of law enforcement.

All of these applications fall under the heading of game theory, which studies situations of strategic interaction. By strategic interaction, I mean an interaction which, when selecting an optimal strategy for yourself, you are directly influenced by the choices (or potential choices) of other actors who are making choices for themselves.

Not all decisions are made in this way. When you go grocery shopping, you aren’t typically particularly concerned with what everyone else is buying. You have a grocery budget, a shopping list, and you pick up what you need. Hence, no strategy involved. This changes when you discuss bidding in an online auction. The decisions on how much to bid and when to bid depend on what other bidders are doing as well – so a smart participant would do his best to anticipate those actions of others when deciding how to proceed.

Game theoretic analysis can become quite complex. In baseball, for example, the pitcher may think “The batter thinks I’m going to throw a fastball, so I’ll throw a curveball instead,” while the batter is thinking “the pitcher thinks I think he’s going to throw a fastball, so thinking that, he’ll throw a curveball, so I’ll get ready for the curveball!” But what if the pitcher knows what the batter is thinking, and throws the fastball anyway? The layers of strategy can build up quickly.

Models of game theoretic situations have been applied in economics, political science, biology, and countless other areas. To simplify these models, there are a few standard components to a game theoretic model that need to be identified:

  1. Who are the players? These can be consumers, governments, businesses, tic-tac-toe players, or political candidates.
  2. What are the available strategies for each player? Strategies can involve affordable bids in an online auction, potential pitches a pitcher can throw in baseball, or available prices a firm can charge.
  3. What are the payoffs to the players? That is, what is the benefit or loss assigned to each outcome? Payoffs can be measured in who wins the game of rock-paper-scissors, the profits made by the firms, or the number of votes each political candidate receives in the election.
  4. How much information is known? Are your opponents’ strategies observable? Are the payoffs known to you?
  5. How does the timing of the game play out? Are moves simultaneous, as in rock-paper-scissors? Are moves sequential, as in checkers?

The study of game theory analyzes theoretical models which incorporate the above components, and most often many additional factors. These models are flexible, and allow economists to think about strategic behavior in myriad of settings. Work in game theory has made substantial contributions to the field of economics in the last 50-100 years, from the well-known work of John Nash to the study of broadband auctions. I hope to post in the future about my own research in game theory – which includes applications in criminal behavior, behavior in team projects, and strategic setting of environmental standards. More to come.

Advertisements

One comment

  1. […] yesterday’s example, the most logical game theoretic prediction is that Alex should accept any deal Eric offers. Even if Eric keeps $40 for himself, and […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: