(4.1) |

For the lower branch, the evaluator is expected to produce:

(4.2) |

These formulas can be verified by looking at the utility function in Section 4.5.1. To find a decision surface between the two alternatives, the points in the belief space at which the alternatives have equal utility are found. There is one solution in this case.

(4.3) | ||

(4.4) | ||

(4.5) |

Therefore, it can be expected that the second agent will lend the car spanner when , and will lend the bike spanner when . Figure 4.4 is a plot of the planner's output, which conforms to expectations. This is the plot for which is identical to the plots for the other training levels, 2, 32 and 128.