Demonstration 3: Clarification

This demonstration returns to look at the second agent's response to the risky strategy. This time, the clarification subtree is added as a third alternative, illustrated in figure 4.7.

Figure 4.7: Game tree for second agent's response with clarification

The utility of the lower branches, lend-car-spanner and lend-bike-spanner is that same as before. Additionally, the utility of the clarify branch is:

$$\begin{split}&u(ask-c) \\ &+ p.(u(ans-c) + u(lcs) + u(ucs) + ... ...+ 100 ) \\ &+ ( 1 - p ).( -1 -10 + 100) \\ \\ = &86 \end{split}$$ (4.9)

Figure 4.8: Utility of strategies against P(intend(car-spanner))

The plot for the planner's output is given in figure 4.8. Notice that in the middle region for p, between 0.2 and 0.8, clarify is the best strategy, but that at the extremes, there is less risk, and so clarification is not appropriate.