Demonstration 2: Upper branch

In the upper branch of the game tree, there are two alternatives available at the second step of the plan. The offer branch is expected to be linear with respect to intend(book-flight-window). In fact the line is flat since each branch has equal utility. It is expected to be constant with respect to bel(have-seat). Therefore the offer branch is constant with respect to both variables.

Figure 4.17: Utility of strategies against P(intend(book-flight-window) and P(bel(have-seat))

The chat branch is followed by a chance node, and so its utility is a weighted sum of two sub curves. The chat sub curve is a constant 101. In the other branch, the agent has a choice between chatting and asking. Chatting gives a constant 86 whereas asking is linear between 80 and 90. Therefore there is a decision surface at 0.6. The plot is given in figure 4.17, with different point styles for the chat and offer alternatives, highlighting their decision surface.

As further verification, the corner points were checked, taking
intend(book-flight-window) in the x position, and bel(have-seat) in the y position.

• At 0,0, 102 is obtained, since the lower branch is taken
• At 0,1, 102 is obtained, since the lower branch is taken
• At 1,0, 87 is obtained, since if the user asks and doesn't get 79 is obtained. but chat obtains 87, so chat is chosen
• At 1,1, 91 is obtained, since the user asks and gets and so the system chooses chat

Figure 4.18: Utility of strategies against P(intend(book-flight-window) and P(bel(have-seat))