# Matrix 2x2

Matrix 2x2 permits any symmetric 2x2 matrix game. Each player chooses their action, a single real number in the range [0,]. The payoff is based on the player's choice and the choice of his or her opponent. The experimenter selects the parameterization of potential payoffs table via the configuration file.

Selectors - The Pure selector displays the payoffs in standard bimatrix form, and forces the player to choose a binary pure strategy, either A (1) or B (0), via a radio button. Below is a screenshot of a one-shot Prisoner's Dilemma, using the pure selector. - The matrix2x2 payoff function also supports the heatmap selector, which allows for mixed strategies. Where the pure selector only two actions, A or B (corresponding to 1 or 0), the heatmap selector allows for any real number in the range [0,].

### Figure 1

A one-shot prisoner's dilemma using the [Pure] selector. This player shown has chosen to cooperate (they have selected action "A") while his counterpart has chosen to defect (action "B").

This has resulted in a payoff of 0 for this player (the cooperator), and 18 for the counterpart player (the defector).

## Configuration

The parameters of the matrix are defined by the fields 'Aa', 'Ab', 'Ba', and 'Bb' in the config file.

The fields 'min' and 'max' do not effect player payoffs, but they do scale the flow payoff chart. The 'min' field defines the smallest value plotted on the Y-axis (0 in this case) and 'max' field defines the largest value plotted on the Y-axis of the payoff chart (17 in the case above).

For example, the Prisoner's Dilemma above is defined by:

 . . . payoffFunction min max Aa Ab Ba Bb ... other config file fields ... . . . matrix2x2 0 17 10 0 18 4 ... other config file fields ...
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