Decision theory, high risk scenarios, etc

Ben Sizer · 2008-02-26T05:39:20

I have a system where several agents have to be arranged into groups to attempt certain abstract tasks, for which a fixed reward is on offer to be shared among the group members if successful. The mathematics of this are chosen so that each additional person contributes less towards the chance of success than the previous one. eg. If one person attempted Task A, he'd have a 50% chance of success, if two people attempted it, the chance would rise to 75%, if three attempted it the chance would become 87.5%, etc. Obviously this means that, given that the expected value for an agent participating in that group drops as the group grows bigger, so they would always opt for smaller groups - a 25% chance of $10 is better than a 90% chance of $1, for example. One factor not yet mentioned though is that these tasks carry risk; failed tasks can be considered dangerous and an agent may be destroyed as a result of that task. Similar to the conclusions of Pascal's Wager, one could consider that any potential reward, no matter how high, compares unfavourably to the chance of death - arguably an infinitely negative penalty - and that therefore the rational decision swings back the other way; all agents should opt for the largest group possible to reduce the risk (assuming they can't just avoid attempting the task altogether). Obviously that is an extreme position, as we daily perform acts with a minuscule but non-zero chance of fatality. But how do we rationalise this? For gameplay reasons, I don't want the agents to always form the smallest group (to earn the most reward) nor to always form the biggest group (to minimise risk), but to come to tradeoffs, based on the amount of reward and the amount of risk. Intuitively, this is how I think humans act, but mathematically, it's hard to see where those two curves cross over. Basically my question therefore is, is there a good way to model this sort of decision making process where people decide that the chance of a high penalty has been reduced to an acceptable level? Can the penalty in this case be adequately measured, and thus compared directly against the reward? (Edit: reworded first sentence to remove emphasis on each agent and more on the group.) [Edited by - Kylotan on February 15, 2008 5:42:59 PM]

Artificial Intelligence Programming

Started by Kylotan February 15, 2008 10:34 AM

30 comments, last by Kylotan 16 years, 8 months ago

Extrarius

1,412

February 25, 2008 12:48 PM

Do I understand correctly that the actual chance of failure at a task is essentially the product of each cooperating agent's chance of failure (or something similar)?

You could take the geometric mean of each agent's ability at a particular task (perhaps omitting excessively low values - agents that wouldn't help much on the task), and use that value in the formula to form an estimate of the number of agents that 'should' be assigned to it, and then choose the agents for each task using weighted random selection (weighting for least failure chance, or to make final selections closer to the mean used for the estimate, or based on potential reward vs the agent's current resources, etc).

"Walk not the trodden path, for it has borne it's burden." -John, Flying Monk

Kylotan

Author

10,513

February 26, 2008 05:39 AM

Quote: Original post by Extrarius
Do I understand correctly that the actual chance of failure at a task is essentially the product of each cooperating agent's chance of failure (or something similar)?

Yes, that is the system I plan to use at the moment.

Quote: You could take the geometric mean of each agent's ability at a particular task (perhaps omitting excessively low values - agents that wouldn't help much on the task), and use that value in the formula to form an estimate of the number of agents that 'should' be assigned to it, and then choose the agents for each task using weighted random selection (weighting for least failure chance, or to make final selections closer to the mean used for the estimate, or based on potential reward vs the agent's current resources, etc).

But say I have 10 agents, and 4 tasks, each of which I determine to require 4-6 agents to be worthwhile. Splitting the agents roughly evenly across the tasks is definitely the wrong thing to do. If I could rank agent/task pairings, I can allocate them one by one, but I'd be concerned about ending up with the agents spread too thinly. Or would that not happen?

Unfortunately, I have far more time available to post here than I do to build prototypes and test this stuff!

[Edited by - Kylotan on February 26, 2008 5:39:02 AM]

Decision theory, high risk scenarios, etc

This topic is closed to new replies.

Popular Topics

Recommended Tutorials

Decision theory, high risk scenarios, etc

This topic is closed to new replies.

Popular Topics

Recommended Tutorials

Reticulating splines