2.7. Computing quantal response equilibria
Gambit provides methods for computing the logit quantal response equilibrium correspondence for extensive games (McKPal98) and strategic games (McKPal95), using the tracing method of (Tur05).
To compute the correspondence, select Tools->Qre. If viewing an extensive game, the agent quantal response equilibrium correspondence is computed; if viewing a strategic game (including the reduced strategic game derived from an extensive game), the correspondence is computed in mixed strategies.
For example, the output of tracing the correspondence for the extensive game of the poker example is shown in Figure 2-21.
The computed correspondence values can be saved to a CSV (comma-separated values) file by clicking the button labeled Save correspondence to .csv file. This format is suitable for reading by a spreadsheet or graphing application.
2.7.1. Quantal response equilibria in strategic games (experimental)
There is an experimental graphing interface for quantal response equilibria in strategic games. Figure Figure 2-22 illustrates the layout of this interface.
The graph by default plots the probabilities of all strategies, color-coded by player, as a function of the lambda parameter. The lambda values on the horizontal axis are plotted using a sigmoid transformation; the Graph scaling value controls the shape of this transformation. Lower values of the scaling give more graph space to lower values of lambda; higher values of the scaling give more space to higher values of lambda.
The strategies graphed are indicated in the panel at the left of the window. Clicking on the checkbox next to a strategy toggles whether it is displayed in the graph.
The data points computed in the correspondence can be viewed
(as in the extensive game example above) by clicking on the
show data icon
on the toolbar. The data points can be saved to a CSV file by
clicking on the
.
To zoom in on a portion of the graph of interest, hold down the left
mouse button and drag a rectangle on the graph. The plot window
zooms in on the portion of the graph selected by that rectangle.
To restore the graph view to the full graph, click on the
zoom to fit icon
.
To print the graph as shown, click on the print icon
.
Note that this is very experimental, and the output may not be very
satisfactory yet.