Airdrop Games

TL;DR

This work develops a game-theoretic framework for designing airdrops to catalyze blockchain launches, linking participant contributions to token value through a technology function and a tokenomics rule. It proves the airdrop game is an exact potential game, enabling clean equilibrium existence and convergence analysis; it then refines equilibrium selection via logit dynamics in both vanishing and finite-noise regimes. The authors apply the model to threshold and Metcalfe-like technology functions, deriving conditions under which good equilibria arise, identifying critical reward levels, and characterizing convergence times. The results offer practical guidance for designers on token allocation, contributor costs, and deployment of partnerchains or multi-token rewards to improve the likelihood and speed of successful launches with meaningful participation. Overall, the framework provides a tractable, theory-backed approach to predicting and influencing launch outcomes in blockchain ecosystems.

Abstract

Launching a new blockchain system or application is frequently facilitated by a so called airdrop, where the system designer chooses a pre-existing set of potentially interested parties and allocates newly minted tokens to them with the expectation that they will participate in the system - such engagement, especially if it is of significant level, facilitates the system and raises its value and also the value of its newly minted token, hence benefiting the airdrop recipients. A number of challenging questions befuddle designers in this setting, such as how to choose the set of interested parties and how to allocate tokens to them. To address these considerations we put forward a game-theoretic model for such airdrop games. Our model can be used to guide the designer's choices based on the way the system's value depends on participation (modeled by a ''technology function'' in our framework) and the costs that participants incur. We identify both bad and good equilibria and identify the settings and the choices that can be made where the designer can influence the players towards good equilibria in an expedient manner.

Figures (7)

• Figure 1: On the left, larger costs $\alpha$ increase the hitting time (100 repetitions 95% confidence). On the right, larger rewards values $\rho$ help to maintain the dynamics above the threshold once it is reached.
• Figure 2: Hitting time for threshold technologies with increasing costs $\alpha$ (same as Fig. \ref{['fig:dynamics-time']}(left) in main text reproduced here for convenience).
• Figure 3: Linear technologies for different $\lambda_V\in\{10,20,100\}$ ($\lambda_V = 1/\tau$, 10 repetitions and 95% accuracy).
• Figure 4: Three different matching pennies games (with choices percentages) as in goeree2001ten.
• Figure 5: Higher airdrop allocations $\rho$ help stabilizing the dynamics in the "high value" region.

Theorems & Definitions (35)

• Example 1: Threshold Technologies.
• Theorem 1
• Theorem 2
• Corollary 1
• Example 2: linear technology with heterogeneous costs
• Theorem 3
• Example 3: rule out bad equilibria
• Theorem 4: Theorem 1.1 in chen2013mixing
• Definition 1
• Theorem 5