# The Balancing Act

## Greed is Good…

*Authored by the **Liquidity Wizard*

# Pair Reactors

This week marks a seminal moment for Tokemak, with the launch of Pair Reactors. Pair Reactors provide the “other side” of the liquidity generated by Tokemak that gets paired with the assets from Token Reactors — for example the ETH or DAI pair asset is used to construct the ABC/ETH or ABC/DAI market for the ABC token.

So to summarize, a Token Reactor takes project/governance tokens from LPs and allows LDs to stake TOKE to direct that liquidity and collateralize the Token Reactor. A Pair Reactor takes stablecoin/ETH tokens from LPs to be paired with the project/governance tokens as liquidity, while LDs in Pair Reactors stake TOKE to collateralize the Pair Reactor.

Tokemak automatically balances the supply of pair tokens (from Pair Reactors) such as DAI, FEI, and FRAX with the supply of assets from Token Reactors. It also optimizes the individual supplies within each grouping, Pair and Tokens.

How is all of this handled? Greed. Er… “economics.” The fundamental assumption of Tokemak is that users will (and should) be maximally greedy. The reward equations that govern Tokemak only pay the maximum global rewards if all participants (Liquidity Directors [LDs] and Liquidity Providers [LPs]) have properly allocated in the pursuit of maximal APR. In this case, Tokemak runs at peak efficiency and there is maximal liquidity from LPs and maximal crowd-sourced liquidity direction and collateralization from LDs.

Put another way, Tokemak emissions are maximal when the liquidity utility is maximal. Tokemak emits according to how useful it is to the DeFi community. If it’s operating inefficiently, the TOKE emissions are lower.

In this article, we will describe how the equations balance three groups of participants: LPs in Token Reactors, LPs in Pair Reactors, and LDs across all reactors.

# Token Reactor LP Equations

The equations that govern Token Reactors have been playing out for the past couple months. Here we finally explain what is going on.

First, let’s define some variables:

· i is the i-th reactor

· lp_token(i) is the % of the overall LP Token Reactor assets in the i-th Reactor (normalized to $ terms)

· ld_token(i) is the % of the LD-staked TOKE to Token Reactors in the i-th Reactor

· r_lp_token(i) is the % of the cycle’s LP Token Reactor rewards that are allocated to the LPs in Token Reactor i

· R_lp_token is the maximum TOKE rewards budgeted to LPs across all Token Reactors each Cycle

· R_lp_token(i) is the quantity of TOKE rewards that LPs in Token Reactor i will earn this Cycle

The % of the overall rewards that go to LPs in Token Reactor i is governed by the following equation:

The following equation can be used to determine the actual rewards for LPs in Token Reactor i:

Currently, LPs in token reactors are eligible for the following maximum rewards:

· R_lp_token = 5600 TOKE per day

The implications of the above equations is that Token Reactor LPs only receive maximal rewards (globally) if the % of Token Reactor LP assets in Token Reactor i matches the % of Token Reactor LD TOKE staked to Token Reactor i.

In layman’s terms, either side controls the other. The equations are coupled. Stake more TOKE to juice the rewards for LPs and attract more tokens to the reactor. Deposit more tokens to juice the rewards for LDs staking TOKE to that reactor. Everything will balance given greedy participants that seek APR.

# Pair Reactor LP Equations

The new Pair Reactors follow a similar structure. Here we define similar variables:

· i is the i-th Reactor

· lp_pair(i) is the % of the overall LP Pair Reactor assets in the i-th Reactor (normalized to $ terms)

· ld_pair(i) is the % of the LD-staked TOKE to Pair Reactors in the i-th Reactor

· r_lp_pair(i) is the % of the cycle’s LP Pair Reactor rewards that are allocated to the LPs in Pair Reactor i

· R_lp_pair is the maximum TOKE rewards budgeted to LPs across all Pair Reactors each Cycle

· R_lp_pair(i) is the quantity of TOKE rewards that LPs in Pair Reactor i will earn this Cycle

The % of the overall rewards that go to LPs in the Pair Reactor i is governed by the following equation:

The below equation shows how to compute the actual rewards for LPs in each Pair Reactor i:

The rewards parameters currently in place are the following:

· R_lp_pair = 2820 TOKE per day

The implications of the above equations is that Pair Reactor LPs only receive maximal rewards (globally) if the % of Pair Reactor LP assets in Pair Reactor i matches the % of Pair Reactor LD TOKE staked to Pair Reactor i.

Tokemak is a kingmaker for stablecoins: the Pair asset with the most TOKE staked to it will naturally attract the most TVL for that stablecoin, thereby appointing that asset the one with the most pairings and liquidity across DeFi.

# LD equations

Finally, let’s look at the LD side of things.

Here we will define the following equations (you see the pattern):

· i is the i-th reactor

· lp(i) is the % of the overall LP assets in the i-th Reactor (normalized to $ terms)

· ld(i) is the % of the LD-staked TOKE in the i-th Reactor

· r_ld(i) is the % of the cycle’s LD rewards that are allocated to the LDs in Reactor i

· R_ld is the maximum TOKE rewards budgeted to LDs across all Reactors each Cycle

· R_ld(i) is the quantity of TOKE rewards that LDs in Reactor i will earn this Cycle

Note that these equations are global: covering assets and TOKE staked across both Pair Reactors and Token Reactors. This is very important to maintain balance.

The % of the overall rewards that go to LDs in Token Reactor i is governed by the following equation:

The below equation shows how to compute the actual rewards for LDs in each Reactor i:

The rewards for LDs are currently set to the following:

· R_ld = 4900 TOKE per day

The implications of the above equations is that LDs only receive maximal rewards (globally) if the % of global LP assets in Reactor i matches the % of LD TOKE staked to Reactor i.

# Final Note

These equations will continue to evolve and expand, and the next big update will balance TVL in Pair Reactors with TVL in Stable Reactors. We will also soon introduce the concept of Reserves and the expanded equations that balance Reserves, Liquidity Providers, and Liquidity Directors in the very near future.

Oh, and debt-liquidity duality will be explained soon…

Discord: https://discord.com/invite/Z5f92tfzh4

Website: https://www.tokemak.xyz/

Medium: https://medium.com/tokemak

Twitter: https://twitter.com/tokenreactor