Initial Liquidity Swaps from a Game Theoretical Standpoint
With the advent of Automated Market Makers (AMMs), which enable the permissionless listing of crypto tokens on a decentralized exchange, it became possible again for projects to bootstrap their development by launching a fungible token. However, some of the mistakes of the ICO bubble in 2017 and 2018 were repeated.
Most notably, the ability to raise millions of Dollars in funding gives project teams an incentive to run off with the fund, rather than to deliver an actual product. Today, this process is called a rug-pull.
Furthermore, the fixed price auction mechanism found in the Initial DEX Offering (IDO) model still requires project teams to come up with their own token valuation, which either causes the IDO to fail (if overvalued), or lead to the hard cap being reached within minutes (if undervalued). In the latter case, this leads to an unfair token distribution, since it is mostly a few whales, who profit from the IDO and ultimately receive a token allocation.
We think that a novel distribution method called Initial Liquidity Swap can both lead to a fairer token distribution and safer incentives that balance the interests of investors and project teams.
Initial Liquidity Swaps
In coordination with our values, InstaLiq DAO seeks to introduce the concept of Initial Liquidity Swap (hereafter ILS). Under this token launch method, a liquidity pool is created where investors bid on a fixed amount of tokens in the style of a batch auction.
During the batch auction period, bidders can at any time increase or decrease their bid as they see fit. Once the auction period runs out, the amount of tokens auctioned off is distributed pro rata among all bidders. Simultaneously, the token is listed on a decentralized exchange using the same amount of tokens on one side, and the total bid amount on the other side.
In result, the total bid amount, driven by market forces, thus determines the initial listing price of the token. At the same time, all bidders swap their bids at exactly the same rate.
The LP tokens resulting from the listing are then sent to a governance-controlled smart contract. This locks the LP tokens permanently, unless they are unlocked by a governance vote, which, for example, might become necessary to move the liquidity to a different AMM. Additional safety measures like time-locks or multi-sig approval can be used to prevent 51% attackers from gaining control over the LP tokens.
The Math Problem of a Fair Token Launch
The commons
The initial trading price of the listed token on the exchange stems from the ILS value process. Let’s define that value at any time t<T by V=sum_i[b_i]/p/2. Where p is the overall initial token supply to be launched, and b_i is the net bid at time t<T of bidder i, b_i=0 if the bidder hasn’t bid at all or has withdrawn all of its previous bid.
V can be considered as the ongoing contested resource value, also known as “the commons”. It represents the auction price of one token. For bidder i, her token contribution at time t<T is defined by v_i=b_i/V.
The commons V is a resource shared by the bidders. It is what economics call a common-pool resource, meaning it is rivalrous (i.e. could be consumed by a single user) and non-excludable (i.e. no user is able to prevent others from consuming it) and its sharing among users comes with a cost for the network in the form of incentives. Such a resource is subject to The Tragedy of the Commons which occurs when individuals neglect the well-being of the network in the pursuit of their personal gain.
Additionally, crypto tokens are also subject to network effects. This can both create positive externalities (from fairly sharing the common resource), or negative externalities (from either excluding individuals from accessing the resource, or not coordinating access to the resource at all).
Specifically, putting a price on tokens — ideally driven by the market forces of supply and demand — creates a positive externality (as opposed to handing out tokens for free within an airdrop), whereas restricting access to the token to a few whale investors (commonly found in fixed price auctions) creates a negative externality.
(Anti)-coordination and cost
A batch auction token launch can be seen as an anti-coordination game, where players have an interest in playing different strategies. Besides, depending on the configuration, or the time in the auction process, it could also be seen as a coordination game where players benefit from playing the same strategy.
For instance, it’s plausible that at the beginning of the auction all players benefit from playing the same Deposit strategy, which creates a positive externality (i.e. the benefit reaped from being in the same network) through the market momentum generated around the token launch. This corresponds to a coordination game.
As the auction progresses however, this common interest may erode and divergent strategies surface reflecting each player’s target relative contribution. For instance, low-net-worth bidders could benefit from steady average-size bids, since the latter preserve a reasonable price upward trend while limiting the impact on the relative contribution. On the other hand, high-net-worth bidders like the so-called whales targeting high relative contribution would rather benefit from no bidding or even steady small-size withdrawals to efficiently mitigate the risk of an overpriced token which would be harmful to large stake holders.
That situation typically leads to anti-coordination mechanisms whereby choosing the same action (e.g. both the above players are bidding) creates a cost rather than a benefit to the network, i.e. a negative externality. That cost is here considered as an overpricing of the token at the moment of swapping.
In its simplest form, the anti-coordination game can be represented by a chicken game with 2 players and 2 strategies: Swerve/Straight (or Hawk/Dove). Transposed to a token launch process, players could be for instance of two types Whale/not-Whale and the two strategies could be Deposit/Withdrawal.
More realistic versions of anti-coordination games are composed of multiple players and multiple strategies. We can cite for instance the crowding game or the congestion game. In the remaining we’ll stick with the chicken game to illustrate the game theory mechanisms at play in a token launch process
(Un)fairness Risks
It is safe to assume that in a classic fixed price token sale auction whales attempt to snatch up a large part of the available supply, which typically leads to the hard cap being reached within a very short time. In result, almost the entire token supply ends up in the hands of only a few investors.
The ILS protocol in its current setup aims to cover against that risk from the first moment of the batch auction up until the last bid. In a chicken game framework, we are trying to prevent the “hawk behavior” from whales in a fixed price auction token sale that may discourage low-value bidders to enter, further reducing their capacity to own a significant part of the supply the more they wait.
In game theory terms, there needs to be some sort of an implicit cooperation among bidders created through incentives, so that the evolutionarily stable strategy (ESS) leading to a Nash equilibrium is a mixed strategy instead of either of the pure strategies (deposit or withdrawal). The reason for this requirement is simple: the pure strategies will almost surely (mathematically speaking) lead to a suboptimal equilibrium because of the negative externality we introduced above (overpricing or destruction).
A mixed strategy is defined by a probabilistic convex combination of the pure strategies. It’s as if players were incentivized to weigh in the utility of bidding and withdrawing to find their own sweet spot instead of going blindly for one or the other, whatever the situation they face.
In token auction terms, this translates into players assigning probabilities to the strategies and then choosing along these probabilities one strategy or the other. So doing, they are “building” their expected payoff function. Probabilities are dependent on the situation players face and on the learning process throughout the game.
To guarantee such a configuration in a game, we need certain technical conditions to be satisfied. Reaching a mixed strategy Nash equilibrium in an anti-coordination game is only possible when (i) the (utility of) cost C of not cooperating (i.e. the negative externality) is high enough (typically greater than V in the maximalist scenario) and (ii) there is no uncorrelated asymmetry (meaning bidders do not know if other players are playing hawk or dove).
The reason for (i) is to ensure the game remains in a configuration where there’s no dominating strategy so that the Nash equilibrium does not imply the same strategy for all players. Such a case happens in the Prisoner’s dilemma where the only Nash equilibrium is the Defect strategy for all players. We would then fall into the Tragedy of the Commons. This would correspond in the auction to an overpricing or a high token concentration in whales, therefore unfair outcome. Instead, we would prefer to remain in a Chicken game where there is no dominating strategy and the game remains inherently adversarial.
The reason for (ii) is to ensure that the ESS is a mixed strategy instead of the pure strategies, mitigating one-way mass behavior from players. That way, the adversarial configuration of the game leads to a fairer outcome because it depends on a probability assignment to the strategies by each player.
Post-ILS Evaluation
Since Initial Liquidity Swaps are an experimental token distribution method, we’d like to use this opportunity to study the behavior of bidders within the batch auction period. Particularly of interest is the bidding behavior of whales at the start and right before the end of the batch auction.
Our hypothesis is that at the beginning of the auction period, bidders will start to “hawk in” to the batch auction pool at least as long as the token is perceived as undervalued, since this constitutes a coordination game whose dominant strategy is to deposit into the batch auction pool.
This will cause the implied token price to rise up to a point where it is perceived as overvalued by the bidders. At this point, an anti-coordination chicken-type game starts, which gives bidders an incentive to “dove out” of the auction pool by reducing or withdrawing their bid. We anticipate that this incentive will become stronger over the time as the batch auction draws nearer to its closing point, prompting the largest withdrawal activities to occur right before the auction closes.
Furthermore, we expect whales to have a larger incentive to dove out before the auction period expires, since they have more at stake in the event of an overpriced swap and are more likely to watch the auction period closely than retail bidders. Ethereum’s gas fees pose an additional incentive for retail bidders to play the hawk strategy, as they are likely better off taking an overpriced token swap, rather than paying the gas fees for a withdrawal. Using the chicken-game analogy, a retail contribution to the batch auction is akin to throwing the steering wheel out of the window, to signal the other driver that he must swerve, or risk a collision.
We measure the fairness of the resulting token distribution by the degree it adheres to the Pareto principle. If 80% or less of the tokens are distributed to the top 20% of bidders, we classify the distribution as “fair”. Based upon this criterion, the LIQ token ILS will have one of three different outcome scenarios:
Worst case (experiment failed)
Whale bidders “hawk in” aggressively right at the start of the batch auction period, thus raising the implied token price too quickly, which creates a deterrent for retail bidders to place their bids. The resulting token distribution shows little to no improvement over fixed price token auctions, meaning that additional measures have to be taken to ensure a fair distribution.
Average case (fair distribution)
Both whale and retail bidders play mixed strategies once the chicken game starts. The resulting token distribution closely follows the Pareto principle.
Best case (superfair distribution)
Most retail bidders play an aggressive hawk strategy before the auction closes, prompting whales to dove out at the last minutes of the batch auction period. The resulting token distribution follows a shallower curve than the Pareto principle would suggest.
Conclusion
InstaLiq DAO is exploring new avenues to push the needle even further towards fairness and meaningfulness of token launch processes. We have shown in this article the game theory mechanisms underneath a token launch and identified incentivization levers that could guarantee a better equilibrium at initial token swapping for the network. Important strides remain ahead for InstaLiq DAO to experiment with these concepts. We are currently exploring various additional incentivization avenues like collection gamification, population structure targeting and custom fairness function. Such innovative tools could potentially make ILS the first reliable engine of mixed strategy Nash equilibrium for token launch.
Thanks to Tobias W. Kaiser for useful comments.
