Author: Paul Veradittakit, Partner at Pantera Capital; Translation: Golden Finance xiaozou

  • A study by Pantera Research Lab found that crypto users exhibited a high present bias and a low discount factor, indicating a strong preference for instant gratification.

  • Quasi-hyperbolic discounting models, characterized by parameters such as present bias (ꞵ) and discount factor (?), help understand individuals’ tendency to prefer immediate returns over future gains, a behavior that is particularly evident in the volatile and speculative crypto markets.

  • This research can be applied to optimizing token distribution, such as airdrops used to reward early users, decentralized governance, and marketing new products.

1 Introduction

A classic Silicon Valley startup story is when PayPal decided to pay people $10 to use its product. The rationale was that if you could pay people to use your product, eventually the value of the network would be high enough that new people would join for free and you could stop paying. This strategy seemed to work, as PayPal was able to continue to grow after it stopped paying, successfully bootstrapping the network effect.

In crypto, we’ve taken this approach and expanded upon it with airdrops, which not only get people involved, but often keep them using our product for a period of time.

2. Quasi-Hyperbolic Discount Model

Airdrops have become a versatile tool for rewarding early adopters, decentralizing protocol governance, and frankly, marketing new products. Formalizing token distribution criteria has become an art, especially when it comes to deciding who should be rewarded and how much value to reward them. In this context, the number of tokens distributed and the timing of the distribution (usually distributed according to a distribution schedule or gradually) both play an important role. These decisions should be based on systematic analysis rather than guesswork, whim, or precedent. Using a more quantitative framework ensures fairness and strategic alignment with long-term goals.

The quasi-hyperbolic discount model provides a mathematical framework to explore how individuals make trade-off choices between rewards at different times. Application of this model is particularly important in areas where impulsive emotions and inconsistencies will significantly affect decision-making over time, such as financial decisions and health-related behaviors.

The model is driven by two population-specific parameters: the present bias (ꞵ) and the discount factor (?).

Current Deviation (ꞵ):

This parameter measures the tendency of an individual to prioritize immediate rewards over disproportionate rewards in the long term. It ranges between 0 and 1, with a value of 1 indicating no present bias, reflecting a time-consistent assessment of the balance of future rewards. As values ​​get closer to 0, an increasingly strong present bias is indicated, indicating a high preference for immediate rewards.

For example, if given a choice between $50 today and $100 a year from now, someone with a high present bias (a value close to 0) would choose the $50 immediately rather than wait to get more money.

and the discount factor (?)

This parameter describes the rate at which the value of a future reward decreases as the time until its arrival increases, suggesting that the perceived value of future rewards will naturally decline with delay. Over longer time intervals of many years, the discount factor can be more accurately quantified. When evaluating two options over short periods of time (less than a year), this parameter exhibits high variability because immediate circumstances may disproportionately influence perception.

Research shows that for the general population, the discount factor is usually around 0.9. However, in groups with a tendency to gamble, this value is often much lower. Research shows that habitual gamblers usually have an average discount factor of just under 0.8, while problem gamblers tend to have a discount factor closer to 0.5.

Using the above conditions, we can express the utility U of receiving reward x at time t as:

U(t) = tU(x)

This model captures how the value of rewards changes over time: immediate rewards are evaluated at full utility, while the value of future rewards is adjusted downward to account for present bias and exponential decay.

3. Exploration Experiment

Last year, Pantera Research Lab conducted a study to quantify the behavioral tendencies of crypto users. We surveyed participants with two simple and direct questions to measure whether they prefer immediate rewards or prefer to obtain a certain amount of future value.

This approach helped us determine representative values ​​for ꞵ and ?. Our results show that a representative sample of crypto users exhibits a present bias slightly above 0.4 and a significantly lower discount factor.

The study showed that crypto users have above-average present bias and low discount factors, suggesting they tend to act impulsively and prefer immediate gratification over future gains.

This can be attributed to several interrelated factors in the cryptocurrency space:

  • Cyclical market behavior: Crypto markets are known for their volatility and cyclicality, with tokens often experiencing rapid fluctuations in value. This cyclicality affects user behavior, as many people are accustomed to speculating in these cycles rather than adopting long-term investment strategies more common in traditional finance. Frequent ups and downs may cause users to discount future value more significantly, fearing that a price drop one day may wipe out their profits.

  • Characteristics of Tokens: The survey specifically asked about tokens and their perceived future value, which may demonstrate ingrained characteristics of token trading. This characteristic is associated with the cyclical and speculative nature of token valuations, underscoring caution about long-term investments in the cryptocurrency space. Furthermore, let’s assume the survey uses fiat currency or some other form of reward to measure preference. In this case, crypto users’ discount rates may be closer to the global average, suggesting that the nature of the rewards themselves may significantly influence the observed discounting behavior.

  • The speculative nature of crypto applications: Today’s crypto ecosystem is deeply rooted in speculation and trading, and these characteristics are prevalent in its most successful applications. This tendency highlights the current user’s overwhelming preference for speculative platforms, which can be seen in the survey results, which show a strong preference for immediate financial gains.

While the results of this study may differ from typical human behavioral norms, they reflect the characteristics and trends of the current crypto user population. This distinction is particularly applicable to projects designing airdrops and token distributions, as understanding these unique behaviors can allow us to better strategically plan and design reward system structures.

Take the example of Drift, a decentralized perpetual contract exchange on Solana, which recently released its native token DRIFT. The Drift team added a time delay mechanism to their token distribution strategy, offering double rewards to users who waited 6 hours after the token was released to claim the airdrop. The purpose of adding a time delay is to alleviate network congestion caused by bots at the beginning of the airdrop, and it is possible to help stabilize token performance by reducing the initial surge of sellers.

In fact, only 7,500 (15% of all airdrop claimants at the time of writing) potential claimants did not wait 6 hours to receive the doubled rewards. Based on the research we presented, if the rewards were doubled in value, Drift could have delayed it by several months and statistically should have been able to appease the majority of end users.