Structural Convergence in Gacha Mechanism Design: An Empirical Taxonomy of Stochastic Reward Systems Against Optimal-Pricing Theory

Gacha monetization systems—stochastic reward mechanisms through which players purchase randomized draws for virtual items—mediate tens of billions of dollars of annual revenue, yet their designs have evolved largely by industry intuition. Recent mechanism-design theory (Gan, 2022) proves that, facing buyers with cumulative-prospect-theory preferences, a revenue-maximizing seller's optimal dynamic mechanism is closely approximated by a hard pity system that truncates the expenditure tail. This theory has so far been validated against only two games. This paper conducts the first systematic empirical test of the prediction across the industry. We formalize each deployed mechanism as a tuple M=({pn},N,q,G,S)M = (\{p_n\}, N, q, G, S)M=({pn},N,q,G,S) of hazard schedule, hard-pity threshold, featured share, guarantee automaton, and spark threshold, and encode 25 mechanisms spanning Chinese, Japanese, and Korean publishers from 2015–2024. For each mechanism we compute the exact distribution of expenditure to a targeted item by dynamic programming and evaluate each distribution under a Tversky–Kahneman (1992) buyer to obtain a certainty-equivalent behavioral markup μ=CE/E[T]μ = CE/E[T]μ=CE/E[T]. Five findings emerge. First, 23/25 deployed mechanisms achieve μ<1μ < 1μ<1, clustered in 0.85–0.98; the two exceptions are structurally distinguished, with pre-2022 Fate/Grand Order (μ=1.068μ = 1.068μ=1.068) being the sole unbounded-tail mechanism and retrofitted with a guarantee in 2022 (μ=0.954μ = 0.954μ=0.954)—a within-title natural experiment supporting the theory. Second, a random-mechanism baseline (3,000 draws from a plausible commercial prior) achieves μ<1μ < 1μ<1 at a rate of 81% overall and 86% among bounded mechanisms, so the deployed sample's 92% share is not statistically dramatic against a mechanism-space baseline (p=0.12p = 0.12p=0.12); the industry's decisive convergence is on boundedness itself, not on cross-sectional optimality among bounded designs. Third, component ablation identifies tail truncation—hard pity or spark—as the causal driver of μ<1μ < 1μ<1: removing tail truncation raises μμμ across seven of eight tested mechanisms, in every case where truncation is the binding constraint. Fourth, sensitivity analysis proves μμμ is invariant to the loss-aversion parameter λλλ, while the value-function curvature βββ dominates: at β=1β = 1β=1, six mechanisms cross μ=1μ = 1μ=1, isolating the specific psychological mechanism on which the theory relies. Fifth, the aggregate time trend in μμμ is directionally consistent with convergence (−0.0034-0.0034−0.0034/year) but not statistically significant (p=0.39,n=25p = 0.39, n = 25p=0.39,n=25). We interpret the industry as having converged structurally to the principle—randomize, but truncate the tail—rather than to a common cross-sectional optimum, and provide the first theoretical treatments of two industry features absent from Gan's model: identity-level "coinflip" guarantees as a price-discrimination interpretation, and strategic hazard obfuscation as a conjectured signaling device.