# Core exchange mechanism

The core exchange mechanism can be viewed as a decision support system which coordinates exchange, governs reversals and handles the main load of disputes in order to significantly reduce arbitration cost and friction versus arbitrated protocols. The mechanism is designed as a sequential game in which Buyer and Seller commit deposits up-front, promoting fair behavior.

## Towards an ideal arbitrated system

Boson Protocol implements a 2-sided deposit structure within a sequential game, which automates the mediation of disputes and mitigates reversal losses by ensuring that both agents are incentivized to behave fairly. However, first we conceive of an ideal system which is highly automated, has minimum viable functionality for coordinating commercial exchange, and in which disputes and reversals are mediated by an ideal arbitrator.

The objective function of the system is:

to maximize the supply of no-complaint voucher redemptions.

The core exchange process proceeds as follows:

• Offer: This involves a seller listing an item; thereby specifying the item’s price and deposit amounts, in addition to the desired payment currency and the listing’s validity period. The Seller’s deposit is then placed in escrow.
• Commit: This involves a buyer committing to purchase an item; thereby paying the seller-defined deposit and the item price, placing both in escrow.

Deposit amounts are variable and form part of the commercial terms of the exchange. Deposit levels are proposed by the Seller and then accepted by the Buyer. It is possible that similar underlying items could be offered via their respective vouchers, but with differing Buyer and Seller deposit levels, indicating different levels of commitment to redemption and quality. We elaborate on this below.

## Practical atomicity

For the happy path, at point of exchange the buyer unilaterally signs a redemption transaction in return for the seller transferring the item. If, and only if, the redemption transaction is signed, the system will transfer the payment amount to the seller. We refer to this as practical atomicity, where practical refers to the assumption that a buyer who signs the redemption receives the item. The transaction is practical rather than absolute, because it is as atomic as handing over cash for goods. With a cash transaction the Seller could take the cash and not deliver the service, but this is not a practical concern. Therefore, we contend that this is atomic enough for most commercial purposes.

## Transaction reversibility

Due to the requirement for atomicity, in addition to the fact that not all promises will be fulfilled, transactions require the property of reversibility. As a consequence, the system enables a Buyer to trigger a refund transaction as well as automatically reversing transactions at expiry of their validity period. The options available after the commit stage are:

• Redeem: This involves the buyer redeeming their purchased item (i.e. gaining ownership of said item). At this point, the payment amount is released to the Seller.
• Refund: This involves the buyer triggering a refund request. Payment is then returned to the buyer.
• Wait: No action taken and the validity period expires. Payment is then returned to the Buyer.

However, transaction reversibility introduces the challenges of reversal costs and dispute mediation identified in the original Bitcoin White Paper. The example of buying a used car illustrates these challenges.

Take the following example:

Alice views a used car online, which is offered for sale at a cost of $10,000 and with 100,000 miles on the clock. Alice makes an offer to Bob of$10,000, which Bob accepts. Alice, who lives in London, agrees to travel the following weekend to complete the exchange with Bob, who lives in Leeds. If Alice fails to arrive in Leeds to complete the exchange, Bob has missed out on other opportunities for exchange, therefore incurring a loss. Conversely, if Alice arrives in Leeds and Bob has already sold the car, then Alice incurs a loss.

## Dispute mediation

If buyer and seller beneficiaries make conflicting claims on real-world events, then smart contracts cannot determine which version of reality to trust. Taking our previous example: if Alice arrives in Leeds to complete the exchange and detects that the car has actually driven 200,000 miles, Alice has a quality dispute. This, and the above, problems are addressed by the mechanism:

The buyer has the option to unilaterally report quality (in addition to other) issues as follows:

• Complain: A Buyer can only complain after either redeeming, refunding or waiting for the validity period to expire. The decision to do this will affect the final deposits payout.

The seller has the option to address issues as follows:

• Cancel or Fault: The Seller can choose to cancel the transaction at any point. However if this is done after the Buyer redeems, then this is considered an admission of fault. This decision will affect the final deposit payouts.

## Summary

The variables that are part of the mechanism are:

• price the buyer is willing to pay for the item, denoted by $$p$$.
• deposit the seller is putting to the mechanism $$M$$, denoted by $$D_S$$.
• deposit the buyer is putting to the mechanism $$M$$, denoted by $$D_B$$.

Therefore, in this setting, there are $$2^3=8$$ final states the contract can observe. Example state is denoted by $$s$$. Contract has to specify $$8\times 2=16$$ transfers, $$2$$ transfers to players for each state $$s$$. One transfer to the seller, denoted by $$t^{S}_s$$, and one to the buyer, denoted by $$t^{B}_s$$. $$T$$ denotes the set of transfers.

Note that the total number of real states is more than $$8$$ since there are hidden actions of the players.

Here, the the green lines denote subgame-perfect equilibrium moves. The red lines denote off-equilibrium moves. Note that the first move is not observed by the mechanism. That is, the states in the left and right subtrees are the same, from the perspective of the smart contract.

In the first move of the seller, H corresponds to sending a high-quality item, while L corresponds to sending a low-quality item.

In the second move, the buyer plays either redeem (R) or no redeem (refund or expire - RfE). In the third move, the buyer complains (C) or does not complain (NC). Finally, the seller acknowledges a fault (CF) or does not acknowledge the fault (NC).

Transfers to players are:

state $$s$$ $$t_s^B$$ $$t_s^S$$
000 $$p$$ $$D_S$$
001 $$p+D_B+0.5D_S$$ $$0.5D_S$$
010 $$p$$ $$0$$
011 $$p+0.5D_S+D_B$$ $$0.25D_S$$
100 $$D_B$$ $$p+D_S$$
101 $$D_B+0.5D_S$$ $$p+0.5D_S$$
110 $$0$$ $$p$$
111 $$0.5D_S+D_B$$ $$p+0.25D_S$$

The first bit stands for redemption, where $$1$$ means that the redemption was performed by the buyer and $$0$$ if it was not. The second bit stands for complaint, where $$1$$ corresponds to the buyer complaint and $$0$$ corresponds to no complaint. The third bit corresponds to Cancel or Fault, where $$1$$ stands for Cancel or Fault and $$0$$ for no Cancel or Fault. Note that there are $$p+D_S+D_B$$ total amount locked up. If transfers paid to players do not sum up to that number, it means that the rest goes to Boson protocol. In the current implementation there are 2 additional states, as CF is allowed to be called any time. If it is called right before buyer’s committment - nothing happens - seller gets his/her deposit back. If it is called right after buyer’s committment - seller gets $$0.5D_S$$ back and buyer gets $$0.5D_S+D_B+p$$.