Airdrop games: towards a theory of tokenomics for blockchain system launches

Blockchain systems are typified by teamwork and collaboration, requiring collective cooperation and contribution to succeed. The concept of 'public good games' has been extensively described in game theory studies. Can it be applied to understanding blockchain tokenomics?

What is unique about blockchains is that the number of engaged participants can be quite large, around the world, without communication or clear, central leadership. What convinces these players, in the game theoretic sense, to contribute¹ to the common good of such blockchain communities? How can incentives be optimally and fairly designed? These questions are pressing, as the practice of distributing tokens to attract participation is widely used in the blockchain space. The recently announced Midnight tokenomics launch, for instance.

Besides intangible reasons (a general belief in the value of decentralized systems for example), potential contributors can have two financial motives: the hope that the tokens will become valuable in the future, and that rewards distributed by the system in the near term could be sold or traded to offset costs.

In a recent paper, accepted to be presented at the 34th International Joint Conference on Artificial Intelligence in August, we study how these ‘airdrop’ rewards affect cooperation in a general but tractable model. We study:

1. what affects the quality of the equilibria, ie the steady states of the system, how easy they are to reach, and their stability once reached,
2. the tradeoffs for the system designer,
3. the token allocation and distribution problem, ie a discussion of who should receive how many tokens.

Modeling airdrops as a game

At the heart of this work is a game theoretic model where users decide whether to engage with a blockchain system after receiving tokens, and how much they contribute to the system. Their decision depends on the cost and benefit of participation, which in turn is shaped by how many others join in (and how much they contribute). This interdependence is captured by a ‘technology function’ that links collective participation to system value, ie to the final value of the token they received from the airdrop.

The designer’s challenge is choosing both the recipients and the amount of tokens allocated to the airdrop in such a way as to lead to a good equilibrium—one where enough users participate to make the system thrive.

To illustrate the model, consider a toy example where a project requires contributions from at least 50% of token recipients to succeed, with the total number being n = 10. If this threshold is met, the system operates correctly, and the token’s value is high, say $10. Conversely, if the threshold is not reached, the system fails, and the token’s value drops to $0.

With an airdrop granting each participant one token and contribution cost being α = $1, two equilibria emerge: (i) no one contributes, since an individual contribution alone does not increase the token’s value but incurs a cost of $1, and (ii) exactly five players contribute. To see the equilibrium at work, observe that if any one of them contemplated not contributing, that would cause the token’s value to drop from $10 to zero (a net profit change from 10 - 1= 9 to zero). Also none of the five non-contributing players has any incentive to do so, since they are already enjoying the high value without any cost. Clearly, the latter equilibrium is preferable, and its existence for higher costs is guaranteed only if the designer sets the airdrop properly (eg for participation costs of α = $20, an individual airdrop of at least two tokens would be required for the same token price).

Our approach allows for different technology functions. We investigate how the nature of the project and the exact way in which contributions are converted to project value affect contributions and, ultimately, success. For example, this analysis can capture network effects: when the presence of one contributor raises the expected payoff from the system for other potential contributors.

Methodology and key results

Our work builds on game theoretic and computer science literature on team projects but refines the classic game theoretic analyses by allowing players to experiment with different strategies, instead of picking with certainty the one strategy they expect to be best. In particular, we use a stochastic rule to assign each player a probability of playing a given strategy (eg contributing or not), which has been shown in empirical applications to describe behavior better than the deterministic rules behind class Nash equilibrium analysis. The logit rule we use assigns a higher probability to strategies with expected payoffs, but also allows for the fact that strategies with similar payoffs will be played with similar frequency.

Intuitively, this stochastic approach—known as the logit response—offers a refinement over pure Nash equilibria by capturing a richer range of possible behaviors, especially when multiple equilibria coexist. It allows us to reason not just about which outcomes are theoretically possible, but about their likelihood. In scenarios like the example above, where both low- and high-engagement equilibria exist, sufficiently large token allocations can make undesirable outcomes (no one contributes) highly unlikely. In this way, the logit model can help designers understand how to shift probability mass toward more desirable system states.

An important finding is that in some cases, the model highlights the importance of commensurate contribution costs to let the system converge to a desired state within reasonable time. What this means is that in these cases there is a type of snowball effect: low costs allow a sufficient number of initial contributions by some players, who then raise the expected return for others, who in turn contribute with a high probability, who in turn raise the expected return for others still and so on. Obviously, this result is particularly relevant when costs are heterogeneous, ie not all players incur the same cost.

Insights and strategic levers

While increasing the amount of tokens airdropped can help improve the quality of equilibria, this lever alone may not suffice. One of the paper’s central insights is that high participation costs can prevent users from coordinating on beneficial equilibria—even when the overall rewards are significant. In these cases, users may opt out simply because they expect others to do likewise, leading to a self-fulfilling low engagement outcome. To counter this, designers have two levers: they can target users with naturally lower costs—such as those already familiar with the technology—or they can reduce barriers to participation more broadly (by streamlining tools or integrating with existing ecosystems, for instance). An example could be enabling current validators on an established blockchain to seamlessly support the launch of a new one.

Looking ahead

Our work is a first step towards formulating the theoretical underpinnings of tokenomics of blockchain system launches - a practice that is observed widely in the blockchain space but still not fully understood from a scientific perspective. For those interested in pursuing further research, there remains a wealth of important questions to study, such as completely characterizing the space of technology functions and mapping them to real world behaviors and operations, introducing external shocks to the model, considering the interactions between multiple systems and participants who engage in multiple launches simultaneously, and cascading multiple launches in the form of a time series. We are actively engaged in continued research on these questions, including all the novel features put forward by the recent Midnight tokenomics whitepaper, and we are looking forward to other members of the blockchain community joining to develop together a complete theory of tokenomics and token policies for blockchain systems.

¹ Contributions can be in terms of individual effort, coding, bug reporting or system maintenance and so on.

Sotiris Georganas, Aggelos Kiayias, and Paolo Penna contributed to this article.