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Achieving economic equilibrium should be one of the primary focus of blockchains and DeFi protocols that seek to perdure
Any situation that involves several parties with different interests and incentives can fall under the scope of game theory. This branch of behavioral economics models the strategic actions of several “players” in a given system that contain a set rules and outcomes. This makes it an effective tool for decision-making in settings such as market dynamics, business, or even personal affairs. The most famous example of this is the well known Prisoner’s Dilemma.
In game theory there exists an outcome where each player will continue with their chosen strategy after taking into consideration the opponent’s strategy and will have no incentive to deviate from it. This state will be the optimal solution for both players, since each player lacks the incentive to change their initial strategy. This state is what is known as Nash equilibrium. Studying systems that have achieved this equilibrium can return insights such as: players acting selfishly could result in a suboptimal choice for both. Or maybe cooperation is not always in one’s best interests. Ultimately there may be an outcome that can be achieved where both competition and cooperation is balanced for mutual benefit.
Speaking of player cooperation, in systems with more than 2 entities, certain strategies may induce a negative outcome for a third player while benefiting the others. This is what is known as collusion, and an example of it in financial markets could be a situation where entities coordinate to influence a market to their own advantage, at the expense of the disadvantage of the market buyers. The most direct example of this practice is price fixing, and yields to market structures of imperfect competition such as oligopolies. The barriers to stop these kinds of activities are usually laws, regulations and government enforcement, something that for better or worse does not apply in the blockchain with its pseudonymity and trustless nature..
For this reason, the economical systems that are developed for blockchains of DeFi protocols have to be as robust and equilibrated as possible, suppressing any chance of situations where a set of entities are more incentivized to collude than to cooperate. In this way all the entities involved will be incentivized to act in their best benefit, which does not negatively impact a third party, such as usually happens, the users of these products. In this article we are going to present two cases where a mutually beneficial outcome has been achieved without detriment for others.
Game Theory In DeFi
The simplest example of a perfect balance is a decentralized exchange such as Uniswap. Two entities engage with it: traders and liquidity providers. It is in the best interest of the liquidity providers to deploy liquidity in those pools that reward the most. This reward is a by-product of the exchanging activity generated by traders. If a set of large liquidity providers would decide to collude and for example not provide liquidity, or provide it to a pool with few usage, they would not earn more than the liquidity providers not cooperating and deploying liquidity by themselves to a pool with high fees.
Same goes for traders, where they get their best return by making use of the pools with the deepest liquidity. This yields to an equilibrium state where both liquidity providers and traders are economically incentivized and aligned. As an exercise to the reader one can think of a third entity as arbitrageurs, and can be concluded how even with this third entity the system remains balanced. This symbiotic relationship can be seen in the “Liquidity Provided” and “Fees” charts of a decentralized exchange, as can be seen in the chart below, the both are highly correlated due to the market mechanics described above:
Volume & Fees and Liquidity Provided of Uniswap v2
The technical and economical mechanics of decentralized exchanges are certainly simpler than other crypto use-cases, such as Stablecoins. The value proposition and raison d’être of Stablecoins is its ability to keep their price peg. The entities involved in this second example are first the own protocol, since it is the one allowing arbitrage around the price by increasing/decreasing supply, and, secondly, other entities would be the stablecoin holders and arbitrageurs. These ones are economically incentivized to arbitrage the price between the ideal exchange rate that provides the stablecoin protocol, and the pools where the stablecoin trades freely. If any of the arbitrageurs would decide not to arbitrage, holders could be severely impacted, and any other arbitrageurs would be increasingly incentivized to arbitrage back the opportunity and earn a higher profit, returning the system back to equilibrium. A visual representation of the frequency that these arbitrages happen can be seen in the chart below, where can be seen Curve’s 3pool, one of the major sources of liquidity for stablecoin arbitrage, and the DAI movements over the last seven days:
DAI’s 3pool transactions historical breakdown over the last 7 days.
The high frequency and activity that the charts show explains how it is highly likely that a market discount on the price of DAI would be picked quickly by arbitrageurs under normal conditions, thanks to the trust deposited in the Maker protocol and DAI constantly trading very close to $1.00.
That would not be the case in a stablecoin such as the UST, where their peg relied heavily on the trading price of LUNA. Such endogenous mechanics opened the possibility of an entity taking economic advantage by shorting the stablecoin and LUNA, benefiting from a lower price on UST the lower that LUNA traded. There is no evidence beyond rumors that this situation really happened in the UST tragedy, but it makes sense to plan carefully for this scenarios before hand, either by minimizing them or by measuring their cost, so they are so costly to perform by a bad player that their probabilities are as close as possible to zero.
To our knowledge, nowadays the industry lacks any standardized model to test for these system imbalances, and so far it is not common to see these topics discussed around, beyond some niche circles. If the DeFi landscape is going to mature, it is paramount to improve its risk management measures, both technically and, as we have seen in this article, economically.
Thanks to Lucas Outumuro and Gabriel Ham for thefeedback and review on the topic.
Nash Equilibrium And DeFi was originally published in IntoTheBlock on Medium, where people are continuing the conversation by highlighting and responding to this story.
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