This forum post is to extend the discussion around the characteristics of Gravity DeX Model.
Lite paper : liquidity/LiquidityModuleLightPaper_EN.pdf at develop · tendermint/liquidity · GitHub
In short, it has three main unique characteristics compared to other existing DeXs.
 it combines AMM(liquidity pool model) with orderbook system
 it does not use CPMM(Constant Product Market Maker), but ESPM(Equivalent Swap Price Model)
 it does not handle orders in serial manner, but in batched auction manner
We hope to continue the discussion about the consequences of these unique characteristics, and explore possible improvement of the model.
Argument : ESPM with Batched Execution significantly increase profitability of pool investors by reducing value extraction by arbitrageurs and dishonest validators
 Reasoning
 Batch execution results in swap price competition among arbitrageurs because it does not prioritize orders by transaction sorting in a block (every order in a batch treated equally)
 Arbitrage orders with more competitive order price will have better chance to be executed
 This order price competition among arbitrageurs will result in swap price which is very close to the global price (less profit chance to arbitrageurs)
 Unlike CPMM, ESPM allows pool investors to accumulate additional profit from price volatility because it is not path independent.
 Path Independency vs Path Dependency
 Assumptions
 There exists no censorship of order transactions
 There exists some order price competition among arbitrageurs
 no cost on swaps(gas fee, swap fee)
 CPMM
 Swap Price = (X+dX)/Y or X/(Y+dY)
 Reserve : X=100, Y=1
 If external price moves 100 → 102 → 100
 Arb swap amount : 1X and 0.01Y
 Swap price : 101 and 100.99
 Result
 Arb profit : (102  101)*1/102 + (100.99100)*0.01 = 0.0098 + 0.0099 = 0.0197X
 Pool investor profit : 0 (path independency)
 ESPM with Batch Process
 Swap Price = (X+2dX)/Y or X/(Y+2dY)
 Reserve : X=100, Y=1
 If external price moves 100 → 102 → 100
 Arb compete each other with order price to get the profit
 Assume that the competition results in swap price with 0.5% price difference against external price
 Arb swap amount : 0.745X and 0.00745Y
 Swap price : 101.49 and 100
 Result
 Arb profit : (102101.49)*0.745/102 + (100100)*0.00745 = 0.003725X
 Pool investor profit
 X → 100+0.7450.00745*100 = 100
 Y → 10.745/101.49+0.00745 = 1.0001
 Comparison
 Arbitrageurs in our model get less profit from price moves because of arb competition and ESPM
 Pool investors in our model get extra profit from price moves
 Assumptions
Challenging Assumptions

Transaction censorship will occur
 When there exists arbitrage opportunity, the block proposer can remove other transactions and include only his/her arbitrage order transaction to avoid competition with other arbitrageurs
 The block proposer can earn arbitrage profit without any order price competition
 If the price difference is d% between pool price and external price, then the optimized order amount is d/4% of pool size
 The expected profit of the block proposer is roughly half of what can be achieved in CPMM

Longer batch period will not prevent the problem
 Assume 20% of validators are dishonest
 Assume one batch is composed of 5 blocks
 Only the last blocks of each batch is at manipulation risk
 Out of 100 blocks, dishonest validators can perform uncompeted arbitrage 4 times
 Compared to 20 times with 1 block batch assumption, the risk is reduced to 1/5

Path dependency is risky ?
 Unlike CPMM, ESPM is path dependent
 (reserves of ESPM  reserve of CPMM) is monotonically increasing for any price path
 Therefore ESPM pool is always safer than CPMM pool
 Hence, ESPM does not open risk exposure by path dependency, but it always accumulates more reserves than CPMM

Forecasting the Effectiveness of ESPM with Batch Process
 Assume 20% of validators are doing this strategy (dishonest)
 For the blocks with honest validators, we assume fairly good competition among arbitrageurs, result in 80% of arbitrageur profit in CPMM can be accumulated in pools
 20%*50% + 80%*80% = 74% of arbitrageur profit in CPMM can be accumulated in pools in ESPM

Arbitrageurs profit and MEV(Miner Extractable Value) is practically not very big
 If it is true, the advantages of ESPM and batch process is not significant
 Is it really not significant? We need statistical analysis on Uniswap
Other Efforts
 To minimize dishonest validators
 We can monitor and compare mempools in public nodes and committed blocks to statistically observe possible censorship from certain validators
 It will not give us hard evidence of censorship, but it can give us good hint about the issue
 Improve consensus algorithm
 Leaderless consensus : there exists no single block proposer
 Additional transaction included in the block from nonblockproposers
 Threshold encryption : hide contents of transactions to prevent selective censorship
 Do we need to improve consensus only for DeX in Cosmos Hub ?
 DeX Zone is more proper to pursue this kind of goal ?
Disadvantages

More slippage cost to ordinary traders
 Traders pay exactly twice more slippage cost than CPMM
 Cost of swap
 Gas Fee : fixed amount
 Swap Fee : 0.3% of order amount
 Slippage Cost
 CPMM : orderAmount*(orderAmount / poolSize)
 ESPM : 2orderAmount(orderAmount / poolSize)
 When orderAmount/poolSize is small, slippage cost is negligible
 if it is 0.01% then the slippage cost is 0.02% of order amount (0.01%p larger than CPMM)
 if it is 0.1% then the slippage cost is 0.2% of order amount (0.1%p larger than CPMM)
 When orderAmount/poolSize is big,
 the trader is a whale
 the trader is an arbitrageur
 pool is too small

And more?