How does normal form represent a game theory problem?
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.
In game theory, the normal formāalso known as the strategic formāis a method primarily used to represent two-person games.1
This representation utilizes a payoff matrix to model the game's structure. In this matrix:12
* Each row corresponds to a possible strategy for one player.12
* Each column corresponds to a possible strategy for the other player.12
* The entry at the intersection of a specific row and column represents the outcome, or payoff, for each player when those specific strategies are chosen.1
By mapping these outcomes, the normal form allows analysts to determine whether a set of strategies is stable, or in Nash equilibrium, meaning no player can improve their expected outcome by unilaterally changing their own strategy. While extensive-form games focus on the sequential, step-by-step progression of moves, the normal form provides a concise way to analyze the interdependent decision-making process of the players involved.12