Financial Cryptography

Trust me, I'm a banker - how do Alice and Bob trade in a trust-failed world?

A friend proposed a problem with international trust - how do Alice and Bob swap currencies where trust in trade has broken down. Both parties want to complete the transaction, but have no support from 'the system'.

Ordinarily the parties could go to their banks and ask for e.g., letters-of-credit, but in this particular case banking services are frozen or drying up or unreliable. How then to do a swap of value when the only thing left is the basic payments system (one assumes that the banks have managed to keep that running...).

Imagine Alice has 1m of A$ to swap with Bob's 1m of B$. The quantities and currencies are uninteresting. What is interesting is that both parties have committed, but one will lose their head if the other does not follow through.

To borrow an idea from cryptographic bit-commit protocols, they could do it in tranches, which is what financial people call bits. It would go like this: Alice sends 10k to Bob. Bob returns with his 10k. And so on, until it is all done, 200 transactions in all.

This would work, but it might be possible to do better. Notice above that Alice is always neutral or at risk, while Bob is always neutral or positive. Also, Bob is learning to trust Alice, but Alice has no such reward.

Overall, we are talking about both risk & trust. On taking a risk, successfully, trust is built. With equal tranches, we have reduced the total risk overall, and increased trust, but we've done it in an asymmetric fashion. We could talk about balancing and benefiting from this.

How about this: Alice goes first, and this puts Bob in the driver's seat, so right now he is taking no risk! So Bob could return the favour. To do that, he could return with 20k. Bob now has matched Alice's contribution, and has now taken on the same risk as Alice had in her first round.

What does Alice return? She is now ahead by 10k. But she has received 20k, so her risk is actually not so bad. If she were to likewise double up, she could send 20k. Alice and Bob have now entered tit-for-tat, each taking on a risk of half their tranche.

Perhaps we could ramp it up more? Consider taking each risk position and rewarding it by ramping it up by a positive multiplier:

1. Alice sends 10k. Bob sends 30k - his risk is now at 20k, greater than Alice's original risk, so she is rewarded for her initial play.
2. Alice now holds 30k for only 10k exposure. So she should send 20k to catch up to Bob, 20k to meet his risk, and another 20k to double the risk, being 60k in total.
3. Bob now holds 70k received and has sent 30k. He should send 40k + 40k +40k = 120k.
4. Alice holds 150k and has sent 70k. She should send 80k * 3 = 240k.
5. Bob holds 310k, has sent 180k. He sends (H - S) * 3 = 390k.
6. Alice now holds H = 540, and has sent S = 310. She sends 690.
7. Bob now holds 1m. He should send 460, which is the lesser of outstanding balance and her straight formula.

From the above, a formula emerges. Each round (except first and last) should transmit (H - S) * R where H is the sender's holdings, S is the receiver's holdings, and R is the risk multiplier.

Risk multipliers are interesting. With R of 1, the initiator is always at risk, the follower is always with zero risk, catching up. But with R of 2, the follower matches her risk, not however extending it, so it quickly moves to balanced, symmetric exposure - tit-for-tat in a positive way. This is perhaps the comfortable compromise.

With R of 3, Bob extends and rewards Alice's initial risk, by taking on new risk that goes well beyond what he need do. This has the advantage of reducing the transactions from o(100) to o(10), and giving the economists an enjoyable chance to show the precise logarithmic reduction that applies.

Some comments on wider issues.

Each exchange could agree on what R or risk parameter they desire. And here we reach some interesting questions in negotiation -- who goes first? Who selects R? Also who selects the initial amount I? Mechanism design might suggest that out of such a negotiation, a fair split in parameters might emerge. E.g., like cut & choose. Or maybe it is a matter for parties to choose.

Also, there is a last round issue. The person who sends the last payment has an incentive to hold. Therefore the formula above might be modified to take account of the ceiling in payments, perhaps reducing the penultimate payments so as to require more trust as it gets closer. Especially for R = 3. It could also be balanced such that Alice as initiator is also the last to send.

This would be the game theory way of looking at it. It is important to recognise that contractual aspects would bring in protection as well. For example, I would be looking to publish any parties who do not complete, perhaps making this compulsory with a 3rd party agency. Also one might refer the thing to binding Arbitration, with rights to full publication and fines, including liens on any future transaction on any other member.... Finally, there should be clauses to include the players and their executioners - names and all - so as to limit the cuts in case the other party begs off.

Of course, the game theory aspects should be as strong as we can make them ... leaving the final exceptions to a short sharp dispute resolution process.

Posted by iang at March 4, 2012 09:27 AM | TrackBack