[DennisP]

Well the blockchain still helps with friends, just because it's a convenient and very censorship-resistant public place to post the keys without having to know each other. But there are plenty of other ways to do it.

For the friendless option, don't return all the stake if secrets are submitted despite proof of life. Instead, return a small portion to incentivize reporting, and burn the rest.

[lxgr]

Wouldn't you want the incentive for false coordinators to be as strong as possible?

Otherwise, the coordinator has more to gain by actually coordinating collusion (i.e. secretly pay off shardholders, reassemble the key, monetize what's in it, don't do anything on-chain) than by revealing the collusion in non-iterated games.

[DennisP]

Ok to sum up what I'm thinking: As a stakeholder, I pay a large deposit. I get an immediate payment, and my deposit back after a year. Proof of life happens monthly. If nobody reveals my key after proof of life goes missing, I lose my deposit. If anyone reveals my key despite proof of life in the past month, then 99% of my deposit is burned, and the revealer gets 1% of the deposit.

If I understand right, your concern with this is that the coordinator could pay off shardholders to reveal their shards directly to the coordinator, avoid revealing shards to the contract, and then the shardholders can get their money back.

However, the shardholders do have to worry that the coordinator will go ahead and reveal, collecting that 1% and burning the rest. Or it could be 10%, or 50%, whatever seems sufficiently tempting to coordinators....given the burn risk, the coordinator has to pay >100% to shardholders regardless (assuming non-iterated).

Maximum theft temptation to coordinators is 100% return, but this removes the financial loss to shardholders who simply reveal prematurely on their own. But maybe even losing 10% is sufficient to dissuade that, and then you have to trust coordinators with access to 90% of your funds.

And all this, hopefully, is in the context of the general public having no idea how much economic value the document in question has to a coordinator. In fact, if coordinators routinely pay shardholders more than their deposits, it would pay people to put up lots of worthless documents and collect the payments.