“When Hindsight Isn’t 20/20: Incentive Design With Imperfect Credit Allocation”, John Wentsworth2020-11-08 (Nash eXchange, mechanism design; backlinks; similar)⁠:

A crew of pirates all keep their gold in one very secure chest, with labeled sections for each pirate. Unfortunately, one day a storm hits the ship, tossing everything about. After the storm clears, the gold in the chest is all mixed up. The pirates each know how much gold they had—indeed, they’re rather obsessive about it—but they don’t trust each other to give honest numbers. How can they figure out how much gold each pirate had in the chest?

Here’s the trick: the captain has each crew member write down how much gold they had, in secret. Then, the captain adds it all up. If the final amount matches the amount of gold in the chest, then we’re done. But if the final amount does not match the amount of gold in the chest, then the captain throws the whole chest overboard, and nobody gets any of the gold.

I want to emphasize two key features of this problem. First, depending on what happens, we may never know how much gold each pirate had in the chest or who lied, even in hindsight. Hindsight isn’t 20/20. Second, the solution to the problem requires outright destruction of wealth.

The point of this post is that these two features go hand-in-hand. There’s a wide range of real-life problems where we can’t tell what happened, even in hindsight; we’ll talk about three classes of examples. In these situations, it’s hard to design good incentives/mechanisms, because we don’t know where to allocate credit and blame. Outright wealth destruction provides a fairly general-purpose tool for such problems. It allows us to align incentives in otherwise-intractable problems, though often at considerable cost.

…Alice wants to sell her old car, and Bob is in the market for a decent quality used vehicle…Alternatively, we could try to align incentives without figuring out what happened in hindsight, using a trick similar to our pirate captain throwing the chest overboard. The trick is: if there’s a mechanical problem after the sale, then both Alice and Bob pay for it. I do not mean they split the bill; I mean they both pay the entire cost of the bill. One of them pays the mechanic, and the other takes the same amount of money in cash and burns it. (Or donates to a third party they don’t especially like, or …) This aligns both their incentives: Alice is no longer incentivized to hide mechanical problems when showing off the car, and Bob is no longer incentivized to ignore maintenance or frequent the racetrack.

However, this solution also illustrates the downside of the technique: it’s expensive.

[cf. the exploding Nash equilibrium. This parallels Monte Carlo/evolutionary solutions to RL blackbox optimization: by setting up a large penalty for any divergence from the golden path, it creates an unbiased, but high variance estimator of credit assignment. When ‘pirates’ participate in enough rollouts with enough different assortments of pirates, they receive their approximate ‘honesty’-weighted (usefulness in causing high-value actions) return. You can try to pry open the blackbox and reduce variance by taking into account ‘pirate’ baselines etc, but at the risk of losing unbiasedness if you do it wrong.]

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