Results

An analysis was done for the problem where agent 2 decides whether to tell agent 1. The best utility gain that can be obtained by agent 2 is 50, obtained where agent 1 initially chooses make-omelette but is convinced to choose make-fish by agent 2. This gain is then multiplied by the value of the chance node for have-eggs, so that it ranges from 0 up to 50. The cost of telling is 10, so it would be expected that a decision surface between telling and ending the negotiation would occur where:

$$\begin{split}&50p = 10 \\ \Rightarrow &p = 0.2 \\ \end{split}$$ (5.5)

To check this prediction, the efficiency of asking and passing to allow a tell were plotted for values of $p = 0.8$, and $p = 0.1$. At $0.1$, agent 2 is expected not to use the tell act, and so agent 1 must seize the floor by asking. On the other hand, at $0.8$, agent 2 is expected to use a tell act, and so agent 1 should decline the floor. These results are plotted in figure 5.10.

Figure 5.10: Utility of (left) ask, and (right) pass, at (top) $p = 0.1$, and (bottom) $p = 0.8$

This demonstration provides a good illustration of the dry-land algorithm (see Section 3.4.7). The speaker uses the "propose" form of the ask act (for a definition, see Section 5.3). In response to the ask act, agent 2 must revise his beliefs so that the subject of the ask, tell, is efficient from agent 1's perspective. Therefore it searches the belief space from level 3 upwards, revising bel(have-eggs) at level 3 from 0.1 up to 0.94, and revising bel(have-fruit) a small amount from 0.6 to 0.56 at level 4. Since bel(have-eggs) is now so high at level 3, tell now becomes efficient for agent 2 as well.