Game theory is a mathematical framework that models decision-making in situations where multiple actors interact with one another. One of the most commonly used tools in game theory is the concept of normal form, which allows us to represent a game as a matrix of payoffs.
Normal form is an important concept in game theory because it provides a way to represent a game in a simple and concise manner. In order to draw normal form, we need to know the players, their available strategies, and the resulting payoff for each combination of strategies.
Step 1: Identify Players and Strategies
The first step in drawing normal form is to identify all the players involved in the game and their available strategies. For example, consider a simple game between two players – player A and player B. Each player has two possible strategies – cooperate or defect.
Step 2: Determine Payoffs for Each Combination of Strategies
Once we have identified all the players and their available strategies, we need to determine the resulting payoff for each combination of strategies. The payoff represents the outcome that each player receives based on their chosen strategy and that of their opponent.
For example, let’s assume that if both players cooperate, they both receive a payoff of 3. If one player cooperates while the other defects, then the defector receives a higher payoff of 5 while the cooperator only receives 1. If both players defect, they both receive a lower payoff of 2.
We can represent these payoffs in a matrix where rows correspond to Player A’s strategies and columns correspond to Player B’s strategies:
|Player A||3, 3||1, 5|
|5, 1||2, 2|
Step 3: Label Strategies and Payoffs in the Matrix
Finally, we need to label the strategies and payoffs in the matrix. In our example, we can use C to represent cooperate and D to represent defect:
|C (3)||D (5)|
|Player A||C (3), C (3)||C (1), D (5)|
|D (5), C (1)||D (2), D (2)|
Drawing normal form in game theory is a simple process that involves identifying players and their available strategies, determining payoffs for each combination of strategies, and labeling them in a matrix. This representation allows us to analyze the game and predict the outcome based on the chosen strategies of each player. By understanding normal form, we can make better decisions in various situations where multiple actors are involved.