Rescorla-Wagner Calculator for Equilibria

This applet allows you to quickly compute equilibria of the Rescorla-Wagner model for a particular probability distribution. To use the applet, you:

  1. Click on the button below to start.
  2. Enter the number of variables (not including the context or the effect) in your system, and press "Continue"
  3. Enter the names of the variables and the effect, and the values for beta when the outcome is present, beta when it is absent, and lambda (the maximum associative strength supported by the effect)
  4. Enter the probabilities to complete the matrix. The cells start with descriptions of the probabilities that belong in them. The column and row names provide an additional guide for entering the probabilities: you need to enter P(ColumnName | RowName). So, for example, the cell in the third column, second row, should contain P(Variable2 | Variable1). The cells that are already filled in (with 1.0) cannot be changed.
  5. If you have differing values for the two beta parameters (and you have more than one cue variable), you will also need to input the probabilities of certain conjunctions. Again, the cells start with descriptions of the probabilities for those cells (and the column and row names also provide a way of determining which probabilities go in which cells).
  6. When you have finished filling in the matrix, press "Compute R-W Equilibrium", and a window will display with the unique equilibrium (if there is one), or else tell you if there are infinitely many equilibria.

Note: all parameters and probabilities can be entered either as decimals (e.g., 0.5) or as fractions (e.g., 2/3).

This applet does not allow you to set the alpha (salience) parameters for the variables. If there is a unique equilibrium, then the alphas are irrelevant. If there are infinitely many equilibria, then although the alphas determine the unique equilibrium, I do not know, in general, how to take the alphas into account. (If someone else can figure out the general solution, I will gladly incorporate those formulae into this applet.)

The derivations of the formulae used in this program can be found in my paper, "Equilibria of the Rescorla-Wagner Model," currently submitted to Journal of Mathematical Psychology.

Any comments/errors/suggestions are quite welcome. They should be sent to david@danks.org (David Danks).