Describe the rewards pool

docs/overview.adoc

@@ -33,21 +33,21 @@ position could bankrupt the collateral pool.
 
 Coverage is always paid out in the pool's covered asset.
 
-== The earnings pool
+== The rewards pool
 
-The earnings pool is a collection of different assets that grows as underwriters
-earn fees and refunds.
+The xref:rewards-pool.adoc[rewards pool] is a collection of different assets
+that grows as underwriters earn fees and refunds.
 
-The earnings pool mints a single earnings token, which is periodically
+The rewards pool mints a single rewards token, which is periodically
 distributed to the collateral pool. Each asset in the collateral pool earns
-based on its earnings rate.
+based on its rewards rate.
 
 Over a period of a week, if a collateral pool contains two assets — WBTC at a
-earnings rate of 2, and ETH at an earnings rate of 1 — each will be allocated
-earnings pool tokens at a rate of 2 to 1.
+rewards rate of 2, and ETH at an rewards rate of 1 — each will be allocated
+rewards pool tokens at a rate of 2 to 1.
 
-As earnings accrue, earnings pool tokens can be withdrawn by underwriters and
-redeemed for the underlying earnings.
+As rewards accrue, rewards pool tokens can be withdrawn by underwriters and
+redeemed for the underlying rewards.
 
 = Efficient collateral liquidation
 

docs/rewards-pool.adoc

@@ -0,0 +1,82 @@
+= The rewards pool
+
+A rewards pool is a contract that accepts arbitrary assets and mints a single
+reward token. Recipients of the reward token can at any time turn it in for a
+portion of the rewards in the pool.
+
+A rewards pool maintains a governable list of recipients and relative reward
+rates. For example, a rewards pool might have two recipients — a WETH
+collateral pool, and a WBTC collateral pool, with respective reward rates of 1
+and 2.
+
+Rewards tokens are minted constantly over time and distributed according to the
+relative reward rates.
+
+== Accounting for rewards distribution
+
+Given the above scenario, at rewards pool creation. 3 rewards tokens are minted.
+1 is reserved for the WETH collateral pool, and 2 for the WBTC collateral pool.
+
+Every tick, an additional 3 rewards tokens are virtually minted.
+
+.Virtual rewards
+[frame="topbot",options="header"]
+|==============================================
+|Time | WETH virtual rewards | WBTC virtual rewards
+|1    |1                     |2
+|2    |2                     |4
+|3    |3                     |6
+|4    |4                     |8
+|==============================================
+
+At tick 5, if the rewards rates are changed, say to 1:1, the rewards tokens are
+realized, then the virtual minting continues at the new rate.
+
+.Virtual and real rewards
+[frame="topbot",options="header"]
+|==========================================================================================
+|Time | WETH virtual rewards | WETH real rewards | WBTC virtual rewards | WBTC real rewards
+|1    |1                     |1                  |2                     |2
+|2    |2                     |1                  |4                     |2
+|3    |3                     |1                  |6                     |2
+|4    |4                     |1                  |8                     |2
+|5    |5                     |5                  |9                     |9
+|6    |6                     |5                  |10                    |9
+|7    |7                     |5                  |11                    |9
+|8    |8                     |5                  |12                    |9
+|==========================================================================================
+
+Similarly, any rewards tokens that are exchanged and burned for the underlying
+pool rewards realizes all reward token minting before the exchange occurs.
+
+This structure should make it clear that reward pools scale in the number of
+ongoing reward recipients — with implications for the <<on-chain-efficiency,
+number of assets>> supported as collateral in a coverage pool.
+
+== Relation to collateral pools
+
+A coverage pool has a single rewards pool that receives and manages all
+underwriter earnings. Each single-asset collateral pool is assigned a relative
+rate in the rewards pool, establishing a way for governance to incentivize
+different assets to target a particular pool composition.
+
+If an asset that's accepted as collateral by the coverage pool is intended as
+underwriter rewards, it should first be deposited in the coverage pool, and the
+underwriter token sent to the rewards pool. Following this pattern means a more
+capital-efficient coverage rewards mechanism, though it also means rewards are
+subject to exit markets.
+
+== On-chain efficiency
+
+There are two bottlenecks in efficient runtime on the EVM with this structure.
+
+The first is the number of reward recipients. Each rate change and reward token
+burn require iterating through all recipients, computing rewards, and minting
+tokens. These costs are ultimately shouldered by reward beneficiaries, and place
+a ceiling on the number of simultaneous reward recipients.
+
+The second is the number of assets being rewarded. Anyone can send a reward pool
+whatever tokens they'd like. Instead of using an allowlist or pushing the cost
+onto reward token holders at redemption time, a short denylist can be used to
+avoid mischief, and reward token holders can decide which tokens they'd like to
+be sent at redemption.