I probably should have brought up the inexploitability concept from Inadequate Equilbria; I’m arguing that mistaken premiums are inexploitable, because Carol can’t make any money from correcting Bob’s mistaken belief about Alice, and I want a mechanism to make it exploitable.
Ah, this clarifies the intent.
As you point out, Bob pays $1.25 for the first $50 of risk, which ends up being a wash. Does that just break the whole scheme, since Bob could just buy all the required synthetic risk and replicate the two-party insurance market?
As stated, I think so, but I think that’s a pretty easy fix. I think it works if, any time Bob is going to offer such an insurance policy to Alice at a certain rate, Bob must also offer at least 1x as much synthetic risk for sale under this scheme for all amounts higher than that rate to any other insurer in the market. I’m not sure whether there’s directly any precedent for forcing something to be sold at a certain price to one party as a condition for selling it to another party, though it rhymes with right of first refusal.
One note is that, by forcing Bob to sell risk to Carol, you’re also creating a “cause Alice to break the camera” bounty for Carol. At a 1X multiplier and nontrivial probabilities of loss, that bounty is probably not a very powerful force, but it’s something to be aware of if scaling to much higher multipliers.
In any case, cool mechanism!
Edit: Also, if your concern is that Bob probably doesn’t have the ability to pay out if Alice breaks the camera, forcing Bob to collect additional money now from Carol in exchange for owing even more money if Alice breaks the camera doesn’t necessarily help. Maybe if you make Bob put all of the risk that Carol bought into escrow though? Does put a certain floor on the cost of insurance that has less to do with risk and more to do with interest rates and Carol’s willingness to lose small amounts of money in expectation to lock up the liquidity of her competitor. Again seems unlikely to be much of an issue in practice for >1% chances of insurance paying out and a 1X multiplier.
Ah, this clarifies the intent.
As stated, I think so, but I think that’s a pretty easy fix. I think it works if, any time Bob is going to offer such an insurance policy to Alice at a certain rate, Bob must also offer at least 1x as much synthetic risk for sale under this scheme for all amounts higher than that rate to any other insurer in the market. I’m not sure whether there’s directly any precedent for forcing something to be sold at a certain price to one party as a condition for selling it to another party, though it rhymes with right of first refusal.
One note is that, by forcing Bob to sell risk to Carol, you’re also creating a “cause Alice to break the camera” bounty for Carol. At a 1X multiplier and nontrivial probabilities of loss, that bounty is probably not a very powerful force, but it’s something to be aware of if scaling to much higher multipliers.
In any case, cool mechanism!
Edit: Also, if your concern is that Bob probably doesn’t have the ability to pay out if Alice breaks the camera, forcing Bob to collect additional money now from Carol in exchange for owing even more money if Alice breaks the camera doesn’t necessarily help. Maybe if you make Bob put all of the risk that Carol bought into escrow though? Does put a certain floor on the cost of insurance that has less to do with risk and more to do with interest rates and Carol’s willingness to lose small amounts of money in expectation to lock up the liquidity of her competitor. Again seems unlikely to be much of an issue in practice for >1% chances of insurance paying out and a 1X multiplier.