Game theory is a branch of mathematics that deals with decision-making in situations where two or more intelligent parties are involved. It is used in a variety of fields, including economics, political science, psychology, and biology.
One important concept in game theory is the focal point. In this article, we will explore what a focal point is and how to find it in game theory.
What is a Focal Point?
A focal point is an idea or concept that people use to coordinate their actions in a game. It is not necessarily the most efficient or optimal solution to the game, but rather a common understanding that players use to guide their decisions. A focal point can be anything that both players are aware of and can use as a reference point for their choices.
Examples of Focal Points
Let’s look at some examples to better understand what a focal point is. Suppose you and your friend are planning to meet at a park for a picnic but did not specify where exactly at the park you will meet. You might decide on meeting at the entrance of the park since it’s easily recognizable and known to both parties.
In another scenario, suppose you and your friend are playing rock-paper-scissors but did not specify any rules on how many rounds you will play or who wins each round. You might agree on playing three rounds because it’s the most common number used in rock-paper-scissors games.
These examples illustrate how people often rely on common knowledge or conventions to make decisions when there is no clear solution or rule governing their actions.
How Do You Find the Focal Point?
Finding the focal point in game theory requires both players to have some level of communication and shared knowledge about the game. When there are multiple possible outcomes in a game, finding a focal point can help both players arrive at an agreement that benefits them both.
Here are some steps to follow when trying to find the focal point:
Step 1: Identify the Available Options
The first step is to identify all the possible options available to both players. This could include different strategies, moves, or outcomes depending on the game.
Step 2: Look for Common Knowledge
The next step is to look for common knowledge or assumptions that both players share. This could be anything from a shared language, cultural norms, or previous experiences playing similar games.
Step 3: Choose a Focal Point
Once you have identified the available options and common knowledge, you can choose a focal point that both players can agree on. This could be anything from a specific move, strategy, or outcome that both players feel comfortable with.
Step 4: Communicate Your Choice
The final step is to communicate your choice of focal point to the other player. This will ensure that both players are on the same page and can use the focal point as a reference point for their decisions moving forward.
Example of Finding a Focal Point
Suppose you and your friend are playing a game where you have to choose between two colors – red or blue. If both players choose red, they win $10 each.
If both players choose blue, they win $5 each. If one player chooses red and the other chooses blue, they win nothing.
In this scenario, there are two possible outcomes – either both players choose red or both choose blue. However, there is no clear rule governing their decision-making. To find a focal point, you might look for common knowledge between you and your friend.
Suppose you know that your friend loves the color red and always wears something red when going out. You might suggest choosing red as the focal point since it’s something your friend associates with positively and would likely choose as well. By communicating this choice to your friend, you both can agree to choose red and win $10 each.
In conclusion, finding the focal point in game theory is an important concept that can help both players reach a mutually beneficial outcome. By identifying common knowledge and choosing a focal point that both players agree on, you can coordinate your actions and achieve a successful outcome in the game.