I see the intuition here, but I think the actual answer on how convex agents behave is pretty messy and complicated for a few reasons:
Otherwise convex agents might act as though resources are bounded. This could be because they assign sufficiently high probability to literally bounded universes or because they think that value should be related to some sort of (bounded) measure
More generally, you can usually only play lotteries if there is some agent to play a lottery with. If the agent can secure all the resources that would otherwise be owned by all other agents, then there isn’t any need for (further) lotteries. (And you might expect convex agents to maximize the probability of this sort of outcome.)
Convex agents (and even linear agents) might be dominated by some possiblity of novel physics or similarly large breakthrough opening up massive amounts of resources. In this case, it’s possible that the optimal move is something like securing enough R&D potential (e.g. a few galaxies of resources) that you’re well past diminishing returns on hitting this, but you don’t necessarily otherwise play lotteries. (It’s a bit messier if there is competition for the resources opened up by novel physics.
I see the intuition here, but I think the actual answer on how convex agents behave is pretty messy and complicated for a few reasons:
Otherwise convex agents might act as though resources are bounded. This could be because they assign sufficiently high probability to literally bounded universes or because they think that value should be related to some sort of (bounded) measure
More generally, you can usually only play lotteries if there is some agent to play a lottery with. If the agent can secure all the resources that would otherwise be owned by all other agents, then there isn’t any need for (further) lotteries. (And you might expect convex agents to maximize the probability of this sort of outcome.)
Convex agents (and even linear agents) might be dominated by some possiblity of novel physics or similarly large breakthrough opening up massive amounts of resources. In this case, it’s possible that the optimal move is something like securing enough R&D potential (e.g. a few galaxies of resources) that you’re well past diminishing returns on hitting this, but you don’t necessarily otherwise play lotteries. (It’s a bit messier if there is competition for the resources opened up by novel physics.
Infinite ethics.