# 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.