Game Theory
Game Theory is a brand of Economics (and decision mathematics) that looks at the different strategies a player (a person making a decision) can make. The main pioneer of Game Theory was John von Neumann whose book and work published in 1928 created the subfield of Game Theory. John Nash also created the theory of a Nash equilibrium, a point were both players have no incentive to adopt another decision.
The different decisions a player can make are given in a payoff matrix. Usually convention dictates that the player listed in the row has his outcomes stated first. For example:

B Plays 1 
B Plays 2 
A Plays 1 
(2,7) 
(4,9) 
A Plays 2 
(3,1) 
(5,5) 
If A plays 1 and B plays 1 then the outcome is 2 units for player A and 7 units for player B. Payoff matrices may also be zerosum, this means that one players gain is another's loss. An example of a zerosum payoff matrix:

B Plays 1 
B Plays 2 
A Plays 1 
5 
7 
A Plays 2 
3 
4 
For a zerosum game, the payoff matrix usually only gives the payoffs for one player (as for the other player the payoff will be the value*1), conventionally this is normally Player A (the player represented by the rows) unless otherwise stated. Below is the same payoff matrix as above, but the payoffs are for player B; note, to find this we have simply multiplied each cell by 1.

B Plays 1

B Plays 2

A Plays 1

5 
7 
A Plays 2

3 
4 
Keywords
Nash Equilibrium  A
situation where no player has a reason to change their strategy.
ZeroSum Game  A zerosum game is one in which one players gain is the other players loss. The payoff matrix is usually given in terms of Player A, to find out Player B's payoff matrix multiply each cell by 1.
Play  The choice or decision made by a player.
Saddle Point  A point where it isn't advantageous to adopt a different strategy, this will only occur if the row maximin = column minimax.
Maximin  The Maximum value of the Minimum outcomes from choosing a play. The maximin is usually found for the rows.
Minimax  The Minimum value of the Maximum outcomes from choosing a play, this would be used to find the best choice for a Player B (column player) in a zerosum game.
Dominate  A row or column dominates another row or column if every single cell has a better payoff.
Play Safe Strategy  A strategy where a player plays the choice that results in him losing the least. This can be obtained by calculated the worst outcome in each row/column and then selecting the maximum value of these worst outcomes.
PayOff Matrix  A matrix representing the payoffs to the players for playing a certain decision.
Stable Solution  See Saddle Point
