The strategic form is for use in experiments that investigate strategic behavior between two players. Games defined in this form have a bi-matrix representation. The designer defines the dimensions and elements of each matrix, two payoff elements per cell. The moderator conducting the experiment determines the number of rounds in each game, and thus defines the number of strategies for each player, and their payoffs at the end of the game. In experimental sessions subjects are paired off according to a protocol determined by the moderator. One player in a typical pair chooses the column of the matrix, the other simultaneously chooses the row, and then they receive the corresponding payoff element that respectively applies to the row and column player.
The discrete form is based on the concept of a game tree, as defined in non-cooperative game theory. In the discrete form, several trees may be drawn, each tree representing a stage in the game. Probability transition vectors connecting the trees determine how likely a given tree will be repeated, direct play from one tree to another, and also define the probability the game will end. The discrete form is more flexible than the extensive form. It allows designers to construct a game in extensive form from a single tree, and thus relate each game history to a unique terminal node. Alternatively designers may exploit the parsimony of a Markov representation, by using several trees linked by their probability transitions.