The Game Theory of Concentrated Liquidity

3 min readNov 10, 2021


The first installment in our new series, “DeFi in Perspective”, by our newest team member, Banditx0x.

“Show me the incentive, and I’ll show you the outcome.”

A central task for Automated Market Makers is to distribute liquidity more intelligently and with higher capital efficiency. You could separate the approaches to liquidity optimization into two categories:

  1. Use mathematical ingenuity to create the perfect liquidity curve for different scenarios.
  2. Give liquidity providers flexibility in how they distribute their liquidity and rely on the collective wisdom of the market to optimize the liquidity distribution.

The first approach means that different protocols specialise in different types of swaps. Curve, for example, specializes in swaps between stable assets — assets which remain at approximately the same price relative to each other.

Cyclos and Uniswap V3 use the second approach. Dan Robinson calls Uniswap V3, “the Universal AMM”, because allowing liquidity providers to distribute their assets on any part of a simple x*y=k curve creates a situation whereby any price curve structure can be imitated. Uniswap can facilitate trades between stable pairs, popular pairs and exotic pairs and remain competitive with other protocols without specializing.

Some of the customizable options Uniswap allows are:

  • Allowing any ratio of assets rather than forcing a 50/50 split between assets
  • Allowing liquidity to be concentrated on specific portions of the price curve
  • Choosing the fees charged on each transaction (0.05%, 0.3% or 0.1%)

Aggregating the liquidity of LPs acting independently and selfishly under these conditions will create a price curve which imitates a very well crafted top down design. Here’s how the game theory works:

In theory we should see very efficient liquidity distribution given these incentives, but does it work in reality? Let’s look at the Uniswap WBTC-ETH pool as a case study:

The histogram on the right of the picture above displays the liquidity distribution of WBTC-ETH. As predicted, the liquidity is concentrated around the current trading price. It gradually tapers downwards on either side, meaning there will still be liquidity when the price shifts. The fee tiers are displayed on the left. 80% of people selected the 0.3% fee tier, which is competitive with the fees charged by other decentralized exchanges. The 19% who picked the 0.05% fee are unlikely to make profits in the long term after factoring in impermanent loss. This practical example shows that while Uniswap LP strategies are not perfectly optimized, they are still better than other solutions currently available.

We should expect the Uniswap V3 model to continuously improve relative to static price curves as it becomes implemented in lower gas fee environments and understanding liquidity provider strategies become more optimized. It is likely that liquidity provision would gradually become a task performed by professional market makers who dynamically shift positions rather than cling to passive yield farming strategies.

Uniswap V3 is currently limited by the high gas fees in Ethereum. Adding extra “ticks” of liquidity costs gas, and thus Uniswap limits the granularity of ticks they allow. High gas also disincentives active management of liquidity, so liquidity providers are more reluctant to change positions in line price shifts. Cyclos brings the Uniswap V3 model to Solana, and its lower gas fees should incentivise more optimal liquidity curves.

We are working on a concentrated liquidity solution at Cyclos. Check out our work at

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