I am bidder E. Whoever bidder G is, they make more profit than I do on average, but I win 25% of the time and they only win 20% of the time.
My method was to interleave two bidding strategies, trying to either spend 300sp at a decent ROI, or spend less on an ROI high enough to beat whoever ended up spending 300sp at a not-quite-as-good-ROI-as-my-original-target.
I am favored to win all heads-up matches, but I never am never favored to win a 4-way with real players. G wins all but one of those, and F wins more 2nd-place finishes in those than I do. So I’m heavily reliant on A/B/NPC being present to make the matchups look more like head-to-head than 4-way.
Looks like my incorrect speculations on the exact models were likely not helpful, I also did not expect the 1 bidders (fine strategy against real duplicates like in the scenario given, but we’re trying to have a competition here!).
It* requires less effort because ‘cooperation’ reduces effort, while ‘competition’ increases it**.
In general, one would define cooperation in games as strategies that lead to better overall gains, and ignore effort involved in thinking up the strategy. In this case, there was an easy cooperative strategy, but it’s not in general true, for example, in the Darwin Game designing a cooperative strategy was more complicated than a simple 3-bot defect strategy. 3-bot didn’t do well but possibly could have if there were a lot of non-punishing simulators submitted (there weren’t).
Also, even in this particular case, you could have had better results if you had taken the effort to get more to follow the same strategy. The rules did not explicitly forbid coordination, even by non-Lesswrongers, so you could have recruited a horde of acquaintances to spam 1-bids. (that might have been against the spirit of the rules, but you could have asked abstractapplic about it first I, I guess).
In general, one would define cooperation in games as strategies that lead to better overall gains, and ignore effort involved in thinking up the strategy.
You should change your username to ‘one’ then.*
Imagine a game where the ‘optimal strategy’ is more difficult to calculate than the optimal strategy in chess. Or, suppose you’re playing a chess game. You know how to calculate the optimal strategy. Unfortunately, it will take 10 years to calculate on your supercomputer, and you can’t take 10 years to make the first move. To neglect time as a resource is to neglect that ‘the optimal strategy’ must be executed after it is formulated, not before.
The rules did not explicitly forbid coordination, even by non-Lesswrongers, so you could have recruited a horde of acquaintances to spam 1-bids. (that might have been against the spirit of the rules, but you could have asked abstractapplic about it first I, I guess).
Do you want to make a bet concerning abstractapplic’s response to this question?
Vague price sense > guessing how others might bid > guarding against someone aiming for significantly higher ROI than you did > exact price sense, I think?
Yeah, and actually 1-bidding can be a good strategy even from a selfish perspective if you can get enough people to coordinate on it, since a small enough number of high bidders will run out of money and the 1-bidders make a large profit on what they do win, though it’s not stable against defection (2-bidders win in the 1-bidder-filled environment).
Of course not, they lose to 3-bidders. I wouldn’t consider that “defection” in the same way though, since the 1-bidding is presumably an attempt at coordination and the 2-bidding would be exploiting that coordination and not directly a coordination attempt.
There weren’t any 2-bidders.
Sure, but if 1-bidding were to become popular in similar problems, there would start to be 2-bidders.
I am bidder C above. Mostly I was trying to win the Jewel Beetle and hope for a lucky roll. I was expecting a larger number of entries and was optimizing for chance to win rather than expected profit. I didn’t put a ton of effort into modeling the exact EVs of the lots, and many of my bids were adjusted to be slightly above the nearest multiple of five.
Same here as “D”—given a goal of “score highest” winning a high value Beetle auction was the best way to do it. I did try to tweak my valuations such that I would either win a bunch of auctions up front, and then not be able to bid on Beetle, or not win the early auctions, and then have a chance at a Beetle win.
Sadly, the EV (excluding beetle) was only ~600 sp, so there was no manipulation of “let others win the first few auctions, then when they run out of money clean up with low bids at the end”
The Jewel Beetle was weird. It was what, like 8% to auto-win everything by winning the Beetle? Except there was just one roll, overall. So in each group of four, one person auto-wins, and then it becomes a cross-group auction where whoever got the Beetle for way less ends up winning. Seems like with very few people participating overall, going for the Beetle caps your odds of winning at 8%, which is not great. With very many people participating, like 100, going for the Beetle caps your odds of winning at the chance there is not a cohort with pure non-beetlers, otherwise whichever of them wins the beetle probably just wins.
Very good points. I actually made a counting error, and estimated the odds of Beetle Wins at ~20%
And then also failed to account for more than 4 players.
Here are the average profits and win rates if we re-ran the sim many times:
I am bidder E. Whoever bidder G is, they make more profit than I do on average, but I win 25% of the time and they only win 20% of the time.
My method was to interleave two bidding strategies, trying to either spend 300sp at a decent ROI, or spend less on an ROI high enough to beat whoever ended up spending 300sp at a not-quite-as-good-ROI-as-my-original-target.
I am favored to win all heads-up matches, but I never am never favored to win a 4-way with real players. G wins all but one of those, and F wins more 2nd-place finishes in those than I do. So I’m heavily reliant on A/B/NPC being present to make the matchups look more like head-to-head than 4-way.
Bidder G reporting in…
Looks like my incorrect speculations on the exact models were likely not helpful, I also did not expect the 1 bidders (fine strategy against real duplicates like in the scenario given, but we’re trying to have a competition here!).
How much time did you spend coming up with that strategy?
Good point. I should have anticipated strategies that require less effort to be more popular.
Returns on time aside (I meant that question seriously—plotting out a returns on compute versus compute (time) curve sounds interesting***):
It* requires less effort because ‘cooperation’ reduces effort, while ‘competition’ increases it**.
(This is also measurable in the split between the traveler and the players.)
*The strategy
**effort
***In particular, getting a sense for something like the marginal returns on time invested, and then comparing it across problems.
In general, one would define cooperation in games as strategies that lead to better overall gains, and ignore effort involved in thinking up the strategy. In this case, there was an easy cooperative strategy, but it’s not in general true, for example, in the Darwin Game designing a cooperative strategy was more complicated than a simple 3-bot defect strategy. 3-bot didn’t do well but possibly could have if there were a lot of non-punishing simulators submitted (there weren’t).
Also, even in this particular case, you could have had better results if you had taken the effort to get more to follow the same strategy. The rules did not explicitly forbid coordination, even by non-Lesswrongers, so you could have recruited a horde of acquaintances to spam 1-bids. (that might have been against the spirit of the rules, but you could have asked abstractapplic about it first I, I guess).
You should change your username to ‘one’ then.*
Imagine a game where the ‘optimal strategy’ is more difficult to calculate than the optimal strategy in chess. Or, suppose you’re playing a chess game. You know how to calculate the optimal strategy. Unfortunately, it will take 10 years to calculate on your supercomputer, and you can’t take 10 years to make the first move. To neglect time as a resource is to neglect that ‘the optimal strategy’ must be executed after it is formulated, not before.
Do you want to make a bet concerning abstractapplic’s response to this question?
*I expect
Neo hasn’t been taken yet.
What I wrote to abstractapplic:
Yeah, and actually 1-bidding can be a good strategy even from a selfish perspective if you can get enough people to coordinate on it, since a small enough number of high bidders will run out of money and the 1-bidders make a large profit on what they do win, though it’s not stable against defection (2-bidders win in the 1-bidder-filled environment).
But:
are the 2-bidders stable against ‘defection’?
There weren’t any 2-bidders.
Of course not, they lose to 3-bidders. I wouldn’t consider that “defection” in the same way though, since the 1-bidding is presumably an attempt at coordination and the 2-bidding would be exploiting that coordination and not directly a coordination attempt.
Sure, but if 1-bidding were to become popular in similar problems, there would start to be 2-bidders.
I am bidder C above. Mostly I was trying to win the Jewel Beetle and hope for a lucky roll. I was expecting a larger number of entries and was optimizing for chance to win rather than expected profit. I didn’t put a ton of effort into modeling the exact EVs of the lots, and many of my bids were adjusted to be slightly above the nearest multiple of five.
Same here as “D”—given a goal of “score highest” winning a high value Beetle auction was the best way to do it. I did try to tweak my valuations such that I would either win a bunch of auctions up front, and then not be able to bid on Beetle, or not win the early auctions, and then have a chance at a Beetle win.
Sadly, the EV (excluding beetle) was only ~600 sp, so there was no manipulation of “let others win the first few auctions, then when they run out of money clean up with low bids at the end”
The Jewel Beetle was weird. It was what, like 8% to auto-win everything by winning the Beetle? Except there was just one roll, overall. So in each group of four, one person auto-wins, and then it becomes a cross-group auction where whoever got the Beetle for way less ends up winning. Seems like with very few people participating overall, going for the Beetle caps your odds of winning at 8%, which is not great. With very many people participating, like 100, going for the Beetle caps your odds of winning at the chance there is not a cohort with pure non-beetlers, otherwise whichever of them wins the beetle probably just wins.
Very good points. I actually made a counting error, and estimated the odds of Beetle Wins at ~20% And then also failed to account for more than 4 players.