The notary contract

In the simplest case of a software wallet executing a cross chain swap.  

The notary can simply watch the ledgers and verify its client goodies have been registered, subject to the price of rollback under timeout.  Bad actors can spoof, make the counter party wait while the cost of roll back increases. Notaries that allow bad behavior get shunned as parties post their notaries prior to engagement.

Notaries end up doing a  long form aggregation of the market, the common pooling effect happening in prices for services. The other method is the pit boss making mass market.  A pit boss being an odd form of notary, it verifies publicizes to all parties what the matching queue structures look like. Then mashes prices, but there is no timeout for reversal, except your opportunity for one last adjustment of your bet. The bit error residual is an ex post verification that pricing was within bounds, like a ledger with slight error.  We should readily prove that the roll back price variation in over the counter protocols matches bit error in the pits. Both should have equivalent tradebook uncertainty.

Networks finite, optimally congested is unique maximizing entropy. 

Now the company to watch  in the market is Republic Protocol.  Those folks are all about swarmulating bot protocols, they would utilize the generic escrow router to its maximum.  They will optimize notaries to allow sufficient lower bounds on roll back fees such the the fails to deliver  queue shows price, secretly discovered in hidden deals.

Then you have Ripple and their fiat customers, no swap, no bearer fiat cash; a non starter for fiaters. So, we have fun times  seeing both hedgers and fiaters playing on even field.