Evaluation example

To demonstrate the evaluation of a game tree, the example used in section 3.4.4 is used (see figure 3.3). Suppose that ask-pair has a positive utility of 15 units, and that each of ask, tell-true and tell-false has a negative utility of 5. To start, a belief state is initialised. Then, passing the ask branch, 5 is subtracted from the utility value. The chance node for the second agent is evaluated at level 2. Suppose this evaluates to 0.4. In the top branch, the proposition in the belief model for agent 2 is updated at level 2 to a value of 1. Next the minimax choice of agent 2 is found, in the context of the agent 2 belief model. This is trivially tell-true. A negative utility of 5 is subtracted here. Since a leaf is reached, the positive utility for goals achieved is computed. This amounts to 15. In the bottom branch, the proposition in the belief model for agent 2 is updated at level 2 to a value of 0, and the subtree is evaluated in the same way as the top branch. The top branch returns a total of 10, the lower branch returns 10 and their weighted sum is 10. Subtracting 5 for the initial ask act, the total utility for the tree is 5 units.