Important Terms in Game Theory
As with many areas and topics in finite mathematics, there is a very special and specific vocabulary that goes along with game theory. Here are some important and useful terms that you should know.
- Payoff matrix: A matrix whose elements represent all the amounts won or lost by the row player.
- Payoff: An amount showing as an element in the payoff matrix, which indicates the amount gained or lost by the row player.
- Saddle point: The element in a payoff matrix that is the smallest in a particular row while, at the same time, the largest in its column. Not all matrices have saddle points.
- Strictly determined game: A game that has a saddle point.
- Strategy: A move or moves chosen by a player.
- Optimal strategy: The strategy that most benefits a player.
- Value (expected value) of game: The amount representing the result when the best possible strategy is played by each player.
- Zero-sum game: A game where what one player wins, the other loses; no money comes in from the outside or leaves.
- Fair game: A game with a value of 0.
- Pure strategy: A player always chooses the same row or column.
- Mixed strategy: A player changes the choice of row or column with different plays or turns.
- Dominated strategy: A strategy that is never considered because another play is always better. For the row player, a row is dominated by another row if all the corresponding elements are all larger. For the column player, a column is dominated by another column if all the corresponding elements are all smaller.