Solver rewards

The protocol is currently subsidizing the solver competition on all chains it operates on, by rewarding solvers on a weekly basis (currently, every Tuesday) with rewards paid in COW. Solvers are rewarded based on their performance as solvers (i.e., when participating in the standard solver competition) as specified by CIP-20, CIP-36, CIP-38, CIP-48 CIP-57 and CIP-67. Solver rewards for participating in the price estimation competition and providing quotes that are needed for the gas estimates and limit price computations of market orders are specified in CIP-27 and CIP-36.

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For the interested reader, the main source of truth for the weekly payments to solvers is this Dune dashboard. The dashboard is populated with data aggregated by scripts within the solver-rewards repository.

Solver competition rewards (CIPs 20, 36, 38, 48, 57, 67)

Solver rewards are computed using a mechanism akin to a Vickrey–Clarke–Groves mechanism (a generalization of a second-price auction to combinatorial auctions). First, each solver proposes multiple solutions. Each solution contains a price vector and a list of trades to execute, which can be used to compute the solution's score. The protocol then selects the winning solutions (and winning solvers) using a fair combinatorial auction, which first filters out the solutions deemed unfair and then selects the combination of fair solutions that maximizes the total score of the auction (see here for more details).

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From the protocol's perspective, a solution executed on chain must equal the solver's initial commitment.

The payment to the winning solver $i$ is

$$\textrm{payment}_i = \textrm{cap}(\textrm{totalScore} - \textrm{referenceScore}_i-\textrm{missingScore}_i).$$

Here $\textrm{totalScore}$ is the sum of the scores of all winning solutions in the auction and $\textrm{missingScore}_i$ is the sum of the scores of solver $i$'s winning solutions that reverted. Finally, $\textrm{referenceScore}_i$ is the total score of a counterfactual auction in which all bids from solver $i$ are removed from the set of bids that survive the fairness filtering.

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The payment calculation can result in a negative figure, in which case the solver is required to pay the amount to the protocol.

The payment is capped from above and below using the function $\textrm{cap}(x) = \max(-c_l, \min(c_u, x))$ that is chain-specific, and is determined by the following values:

• Ethereum mainnet, Arbitrum, and Base chain: $c_l = 0.010 \;\textrm{ETH}$ and $c_u = 0.012 \;\textrm{ETH}$,
• Gnosis Chain: $c_l = c_u = 10 \;\textrm{xDAI}$.

Solutions with scores that are non-positive will be ignored. If only one solver submits solutions, $\textrm{referenceScore}_i$ is, by definition, zero. Formally, this corresponds to always considering the empty solution which does not settle any trades and has a score equal to zero as part of the submitted solutions.

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There is no guarantee that the per-auction rewards are greater than the gas costs of executing a transaction. Hence, solvers cover these costs by adjusting their reported score. Of course, a solver who adjusts their score downward too aggressively is then at a disadvantage in the auction. The mechanism, therefore, incentivizes the accurate estimation of gas costs.

Additional solver costs (slippage)

In addition to paying for gas, the winning solver might incur additional costs, such as, for example, negative slippage once a solution is settled on chain. These costs are not an explicit element of the mechanism, but they are relevant in determining the solver's optimal strategy. More precisely, per CIP-17, solvers are responsible for managing potential slippage incurred by the settlements they settle. This is a component that affects payouts, but can be treated completely separately, and we do so in the accounting section.

Solver's strategy

The recommended strategy for a solver is to start by dividing the available orders into groups of orders on the same directed token pairs --- i.e., in each group, all orders have the same sell and buy tokens. The next step is to compute the best possible routing for each group and submit it as a solution. Note that, by construction, each of these solutions will use outside liquidity. Finally, a solver should check whether it is possible to improve these solutions by creating batched solutions containing orders on different directed token pairs. These additional efficiencies may come from, for example, exploiting liquidity already available on the protocol --- using one order as liquidity for the other (in a CoW) or using CoW AMM liquidity --- or from gas savings. Solvers should submit an additional solution for every combination of groups of orders for which additional efficiencies are possible. When submitting such a solution, they should pay attention to sharing the additional efficiencies among all orders in the batch; otherwise, the batched solution may be filtered out as unfair.

As already discussed, solvers are responsible for paying the gas cost of a solution. Also, if a solution reverts, a solver may incur a penalty. Hence, when reporting their solution, solvers should adjust their reported score downward to account for the expected costs of settling a solution on the chain.

Finally, the protocol rewards are specified so that solvers can participate in an auction without misreporting the score they can generate (net of expected costs). This is easy to see if the cap is not binding, and misreporting does not affect $\textrm{referenceScore}_i$. Then, by reducing the reported score of a solution, solver $i$ does not affect its payoff if this solution is among the winners (which only shifts from protocol rewards to pocketed slippage), while reducing the probability that this solution is a winner. It is therefore a dominant strategy to bid truthfully.

The presence of the cap on rewards $c_u$, however, makes the problem more complex as it introduces a "first-price auction" logic: if the difference between the best and second-best solution is very large, then the winning solver wins more when it underreports its score. However, determining the optimal amount of underreporting is very complex and requires each solver to make strong assumptions regarding the performance of competing solvers. There are also some edge cases in which by reducing the score of a solution, solver $i$ can benefit by making the filtering steps less stringent for its opponents (see here for a discussion).

To summarize, truthfully revealing the (cost-adjusted) score that a solver can generate for each submitted solution is optimal if the cap is not binding, and misreporting does not affect $\textrm{referenceScore}_i$. It is not necessarily optimal in uncompetitive auctions when the difference between the best and second-best solution may be large, and in some edge cases in which a solver may benefit from making the filtering step less stringent. However, in these cases, deriving the optimal strategy is a very complex problem. We conclude by noting that most CoW Protocol batches are very competitive --- the cap on rewards is binding only in about 9% of auctions --- and that a solver benefits by making the filtering steps less stringent for its opponents only in sporadic cases.

Price estimation competition rewards (CIPs 27, 57)

The price estimation competition is a separate competition where solvers compete to provide the best response to a quote request. Quote requests look almost identical to single-order batch auctions, where there is only one order with a trivial limit price, and solvers propose executions of this order with the goal to maximize "out amount minus gas costs", in the case of a sell request, or minimize "in amount + gas costs" in the case of a buy request.

As specified in CIP-27, CIP-36 and CIP-57, solvers that participate in the price estimation competition are rewarded for each order that is within the market price, is associated with a quote that was computed as part of the price estimation competition, and was used in order to compute the limit price of the order. The protocol keeps track of the quote associated with each created order and the corresponding solver that provided the quote. If and when the order gets executed, the solver that provided the quote (which can be different than the solver that ended up executing the order) gets rewarded as follows:

• Ethereum mainnet: $\min\{0.0006 ~\textrm{ETH}, 6 ~\textrm{COW}\}$,
• Arbitrum: $\min\{0.0002 ~\textrm{ETH}, 6 ~\textrm{COW}\}$,
• Gnosis Chain: $\min\{0.15 ~\textrm{xDAI}, 6 ~\textrm{COW}\}$,
• Base Chain: $\min\{0.0002 ~\textrm{ETH}, 6 ~\textrm{COW}\}$,

where, again, the conversion from ETH and xDAI to COW is done by using an up-to-date price (specifically, the average ETH/xDAI/COW Dune prices of the past 24h before the payout are used to determine these exchange rates).