Finite Math For Dummies
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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.

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Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.

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