Let’s talk game theory! Game theory can be explained as “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers” (thanks Wikipedia). So when we discuss game theory, we are not talking about video-games. We are talking about decisions that “players” (people, businesses, governments, animals) have to make while taking into consideration the decisions of opposing (or cooperating) “players.” For those who do not have a mathematical background, you can relax. The fundamental concepts of basic game theory can be understood with a minimal math background. Before diving into the subject, a brief overview on the structure of game theory must be explained.
When analyzing basic game theory models, you will usually see the “normal-form representation of games.” The normal form representation of games specifies:
- The players in the game.
- The strategies available to each player
- The payoff received by each player for each combination of strategies that could be chosen by the player.
The term “payoff” can be interchangeable with the term “utility” which is widely used in the field of economics. When we talk about utility we mean the “measurement of usefulness.” For example, let’s say I have the option of going to the movies or an antique store. I value the movies at 6 utils (another way to say utility) and the antique store at 2 utils (sorry fans of antique stores). Since 6 > 2 I would rather go to the movies than the antique store. But with game theory, I could be involved in a game where there is an opposing player who would prefer to go to the antique store than the movies.
Let’s draw this game out using a matrix:
We can summarize this matrix with the normal form representation.
- The number of players in the game is 2 (myself and my mom)
- The strategies are listed for both players. I have two strategies (represented in bold) to choose either movies or antique. My mom also has two strategies (shown in red) of movies or antique.
- Within each cell is a payoff for the players. (My payoffs are bold and my mom’s are red).
So the way to read this is if both my mom and I choose simultaneously to go to the movies then my payoff will be 6 and hers will be 2. If we both choose to go to an antique store, my payoff will be 2 and hers will be 6. If we make the opposite choice from each other then we will both get a payoff of 0 since we would not be together (I would rather go to the antique store than be alone). The above game is an example of Battle of the Sexes which will be analyzed later. This is a simultaneous game since there is no order of which the players must choose.
Let’s look at this other matrix:
If you are player one, which strategy would you choose and why?
We will discuss this game in the next blog.