Dominant strategies are game-changers in strategic decision-making. They always give you the best outcome, no matter what your opponent does. This concept is key to understanding how players make choices in various scenarios.
Strictly dominant strategies always win, while weakly dominant ones are at least as good as other options. Knowing these helps predict player behavior and find equilibrium points in games. It's crucial for analyzing real-world strategic interactions.
Dominance Concepts
Strict and Weak Dominance
- Strictly dominant strategy always yields a higher payoff than any other strategy, regardless of the opponent's choice
- Weakly dominant strategy yields a payoff at least as high as any other strategy, regardless of the opponent's choice
- May have the same payoff as another strategy for some of the opponent's choices
- Strategy dominance occurs when one strategy is strictly or weakly dominant over another
- Dominated strategies are those that yield lower payoffs compared to the dominant strategy
Dominant Strategy Equilibrium
- Dominant strategy equilibrium is a game outcome where each player employs their dominant strategy
- Results in the best possible payoff for each player, given the strategies of the other players
- Occurs when all players have a strictly dominant strategy
- In a two-player game, if both players have a strictly dominant strategy, the game has a unique dominant strategy equilibrium (Prisoner's Dilemma)
Strategic Foundations
Payoff Matrix Representation
- Payoff matrix is a tabular representation of a game's outcomes and payoffs
- Rows represent the strategies of one player, while columns represent the strategies of the other player
- Each cell in the matrix contains the payoffs for both players, given their chosen strategies (Row player's payoff, Column player's payoff)
- Payoff matrices facilitate the identification of dominant strategies and equilibria
Best Response and Strategic Decision-Making
- Best response is the strategy that yields the highest payoff for a player, given the strategy chosen by the opponent
- A player's best response may change depending on the opponent's strategy
- Strategic decision-making involves considering the opponent's potential strategies and their impact on one's own payoffs
- Players aim to maximize their payoffs by choosing the best response to their opponent's strategy
- Rational players are expected to employ dominant strategies when available
- If no dominant strategy exists, players consider their best response to the opponent's strategy (Battle of the Sexes)