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How are strategies represented in game theory?
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game theory
Table 1
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, strategies are represented through three primary formal models, depending on the nature of the game being analyzed:1
- Extensive Form: Used for games that progress step-by-step, this is represented by a "game tree." Each turn is a vertex, and branches indicate the successive choices available to players.1
- Normal (Strategic) Form: Primarily used for two-person games, this represents the game via a payoff matrix. Rows represent the strategies of one player, columns represent the strategies of the other, and the intersections display the outcomes or payoffs for each combination of choices.12
- Characteristic-Function Form: Generally used for games with more than two players, this form indicates the minimum value that any coalition of players can guarantee for itself when playing against the remaining participants.1
These representations allow mathematicians to determine if a set of strategies is stable, such as in a Nash equilibrium, where no player can improve their expected outcome by unilaterally changing their chosen strategy.12