Intelligent Agent Foundations Forumsign up / log in
by Stuart Armstrong 399 days ago | link | parent

I think it does do the double decrease for the known smaller network.

Take three agent \(A_1\), \(A_2\), and \(A_3\), with utilities \(u_1\), \(u_2\), and \(u_3\). Assume the indexes \(i\), \(j\), and \(k\) are always distinct.

For each \(A_i\), they can boost \(u_j\) at the cost described above in terms of \(u_i\).

What I haven’t really specified is the three-way synergy - can \(A_i\) boost \(u_j+u_k\) more efficiently that simply boosting \(u_j\) and \(u_k\) independently? In general yes (the two utilities \(u_j\) and \(u_k\) are synergistic with each other, after all), but let’s first assume there is zero three-way synergy.

Then each agent \(A_i\) will sacrifice \(1/2+1/2=1\) in \(u_i\) to boost \(u_j\) and \(u_k\) each by \(1\). Overall, each utility function goes up by \(1+1-1=1\). This scales linearly with the size of the trade network each agent sees (excluding themselves): if there were two agents total, each utility would go up by \(1/2\), as in the top post example. And if there were \(n+1\) agents, each utility would go up by \(n/2\).

However, if there are any three-way, four-way,…, or \(n\)-way synergies, then the trade network is more efficient than that. So there is a double decrease (or double increase, from the other perspective), as long as there are higher-order synergies between the utilities.



NEW LINKS

NEW POSTS

NEW DISCUSSION POSTS

RECENT COMMENTS

I found an improved version
by Alex Appel on A Loophole for Self-Applicative Soundness | 0 likes

I misunderstood your
by Sam Eisenstat on A Loophole for Self-Applicative Soundness | 0 likes

Caught a flaw with this
by Alex Appel on A Loophole for Self-Applicative Soundness | 0 likes

As you say, this isn't a
by Sam Eisenstat on A Loophole for Self-Applicative Soundness | 1 like

Note: I currently think that
by Jessica Taylor on Predicting HCH using expert advice | 0 likes

Counterfactual mugging
by Jessica Taylor on Doubts about Updatelessness | 0 likes

What do you mean by "in full
by David Krueger on Doubts about Updatelessness | 0 likes

It seems relatively plausible
by Paul Christiano on Maximally efficient agents will probably have an a... | 1 like

I think that in that case,
by Alex Appel on Smoking Lesion Steelman | 1 like

Two minor comments. First,
by Sam Eisenstat on No Constant Distribution Can be a Logical Inductor | 1 like

A: While that is a really
by Alex Appel on Musings on Exploration | 0 likes

> The true reason to do
by Jessica Taylor on Musings on Exploration | 0 likes

A few comments. Traps are
by Vadim Kosoy on Musings on Exploration | 1 like

I'm not convinced exploration
by Abram Demski on Musings on Exploration | 0 likes

Update: This isn't really an
by Alex Appel on A Difficulty With Density-Zero Exploration | 0 likes

RSS

Privacy & Terms