Game theory

Game Theory

Concepts of Game Theory

• Payoff matrix: A table shows the outcomes of each player for every possible combination of strategies they could play.
• Maximin strategy: A strategy where a player chooses the option that maximises the minimum possible payoff.
• Minimax strategy: The strategy where a player chooses the option that minimises the maximum possible loss.
• Dominant strategy: A strategy is dominant if its payoffs are always at least as good as all other strategies, regardless of what other players do.

Pure and Mixed Strategies

• Pure strategy: A situation where a player uses one single strategy.
• Mixed strategy: A situation where a player randomises over multiple strategies, with specific probabilities.

Saddle Points, Value of the Game, and Equilibrium

• Saddle Point: This is a pure strategy equilibrium in a 2-player game matrix. This point gives both the maximin and the minimax.
• Value of the game: The value of the game is the expected payoff to each player when each plays their optimal strategy.
• Nash equilibrium: This is a situation in which each player in a game has chosen a strategy, but no player can change their strategy to improve their payoff given the other players’ strategies.

Zero-sum and Non-zero-sum Games

• Zero-sum games: These are games in which one player’s gain is another player’s loss.
• Non-zero-sum games: These are games in which the sum of payoffs to all players need not be zero – it can be positive or negative.