Lessons on Value of Information From Civ

post by johnswentworth · 2020-10-07T18:18:40.118Z · LW · GW · 6 comments

I’m a big fan of the game Civilization. Civ is the canonical empire-building game: you explore the world, expand your empire, manage your economy, invade other empires, unlock new tech, etc. A few months ago, the game released “tech shuffle mode”, which radically changes the game (and IMO makes it a lot more interesting). Usually, a not-yet-unlocked section of the tech tree looks like this:

To unlock a tech, we first need to unlock the prerequisite techs (in left-to-right order). The tree is the same in every game, so we can plan ahead to unlock key technologies early - e.g. we can ignore the lower half of the tree in order to get to Steam Power faster. But with tech shuffle mode, a not-yet-unlocked section of the tree looks like this:

The tree structure is randomly generated each game (although techs are still grouped by “era”, so e.g. we won’t unlock nukes right at the start of the game). Techs are also hidden until we’re ready to research them (i.e. until we unlock the prereqs). That means, for instance, that we can’t focus resources on techs needed to unlock Steam Power because we don’t know where in the tree Steam Power is.

But there’s a catch: there are actions we can take to reveal a tech in the tree. This is the “tech boost” mechanic - for instance, by finding another civilization, we can “boost” Writing, reducing the resource cost to unlock it by 40% and (more importantly) revealing its position in the tree. It looks like this:

In other words: we can pay to acquire information.

This is especially important when the value of information (VOI) is high. What does that look like? Like this:

There’s several different branches, each several techs deep. The strategically-important tech we want is somewhere at the end of one of those branches, but we don't know where. Brute-force searching all of the paths until we find it would require unlocking ~½ of these techs on average, but if we knew which branch to take, then we’d only need to unlock one branch - i.e. ~¼ of them in this case. So, I can pay some resource cost to reveal my target tech in the tree, and then I can get to it about twice as quickly (on average).

I realized the importance of the tech boost mechanic as a way of purchasing information after my first game on tech shuffle mode. It seemed that VOI was often very high, so I made an explicit effort to pay attention to it in my next few games.

The result: even when explicitly trying to pay attention to VOI, I regularly noticed that I wasn’t investing enough in it.

The basic problem is that VOI isn’t readily visible. I click into the tech tree, and I see something like

… and the natural response is “ok, my options are Animal Husbandry, Mining, or Pottery. Of those, Mining seems most useful right now, since it will let me build mines”. It’s so easy to say “well, I don’t have any information to prefer one unrevealed tech over another, and Mining is the most useful of the visible options, so I might as well start with Mining”. Animal Husbandry, Mining and Pottery are right there, they’re visible, they’re salient, they’re the obvious things to focus on. I have to step back a minute to realize that Animal Husbandry, Mining and Pottery are all basically-irrelevant right now compared to e.g. Shipbuilding, far and away the most important thing is to unlock Shipbuilding, which means the top priority is to figure out where Shipbuilding is. It’s so easy to weigh the visible options against each other, it’s such a natural instinct, but the optimal choice is to ignore the visible, direct consequences of each choice and instead gain more information.

This is, of course, a metaphor for the real world.

The real world is high-dimensional [LW · GW], so VOI is orders-of-magnitude higher than in Civ’s low-dimensional tech tree. There aren’t 4 possible paths to choose from, there are hundreds or thousands at least. The VOI isn’t a factor of 2 cost reduction on average, it’s a factor of 50 or 500 cost reduction. Brute-force work on every project in some random order realistically may never find the one or two big things which matter more than anything else.

It’s so easy to say “well, of all these projects, adding a page for X seems like it would improve our app the most”. Or “well, of all these projects, running ads on Y seems like it would increase our profits the most”. Or “well, of all these projects, trying a standing desk seems like it would increase my productivity the most”. There’s a list of projects right there in front of us, it’s so easy to imagine the direct consequences of each project. But in a high-dimensional world, with high VOI, the optimal choice is usually to ignore the visible, direct consequences of each choice and instead gain more information.

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