I have finally come to one of the most crucial decisions in the design: the evaluation of the desirability of accepting a deal proposal. The actor must choose between three options: accept, reject, or lie (that is, accept the deal with the intention of supplying false information). The three controlling factors are the cost of the deal, the benefits of the deal, and the risks arising from the deal.
The Benefits of the Deal
These arise from the actor’s current state of knowledge. The less certain the actor’s knowledge is, the more valuable the deal. Thus, the actor need merely consult his uncertainty value for the auragon count in question.
However, there is an additional consideration: the actor’s overall state of knowledge of the topic. Example: Joe has this knowledge: for Tom: tanagagon is 2.63 ± 1.7; shialgon is 1.47 ± 2.6; katsinagon is 1.2 ±1.2.
But Joe also has this information about Mary: tanagagon is 1.78 ±0.6; shialgon is 2.13 ±0.9; and katsinagon is 2.22 ±2.8.
Looking at these individually, Joe would select Mary’s katsinagon as the most important value to know. But overall, he knows less about Tom. Therefore, I think that we should use the sum of the three uncertainties to establish the importance of the knowledge, and the uncertainty value itself as another factor in the equation. Here’s my first cut at the benefit equation:
benefit = Blend(BSum3(TanagaUncertainty, ShialUncertainty, KatsinUncertainty), ProposedUncertainty)
Of course, we must also modulate this by the degree of trust we have in the speaker. Information from a known liar has little value.
The Cost of the Deal
This should be based on the threat posed by the other actor. If he’s just about to win, then the cost is high. Also, the cost is inversely proportional to the magnitude of the auragon count to be revealed. You don’t EVER want to tell somebody that another actor has a zero auragon count for any aura; that guarantees that they’ll attack the third party that night.
The danger imposed by another actor is the ratio the sum of that actor’s auragon counts to the average sum of auragon counts for all the actors.
Lying versus rejecting the deal
If a deal looks bad, should the actor reject it or instead accept it with the intention of lying? I think that hinges on two considerations: first, how dangerous that other actor is in terms of winning the game. Obviously, I will need a danger custom operator to handle this task. The other factor is the lateness of the game: the earlier you lie, the more likely it is that the news will spread all through the group.
Of course, this also leads to the possibility that one can lie about lying… too messy for the moment.