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Pay to (Not) Play: Monetizing Impatience in Mobile Games
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Theoretical and simulation study of skip pricing in mobile games where player value for completing grind tasks depends on the rarity of skip usage, showing high prices can yield both high utility and revenue and proposing a simple Myerson threshold pricing scheme with a 1/e revenue approximation.
Problem
Mobile games sell skips to avoid timer-based grinding, yet prices are high and few players buy, which seems incompatible with standard economic models of utility and revenue; the paper asks how skip pricing can give both high player utility and high revenue.
Approach
Players value completing tasks by perceived difficulty, so skip purchases by others degrade the value of achievements. The paper models three player types (fully-sensitive, price-sensitive, insensitive), characterizes whale-like type distributions where utility-optimal and revenue-optimal prices coincide at high levels, and proposes Myerson threshold pricing that takes the minimum of a retention-b
Key results
- Myerson threshold pricing is proven to achieve at least a 1/e fraction of the known-types revenue under MHR marginal value distributions and retention regularity.
- Theorem shows that for any constant c there exist retention and marginal value distributions where known-types revenue exceeds unknown-types optimal revenue by a factor c, so no simple bound holds without distributional assumptions.
- Simulations show lower prices usually perform better; scaling the Myerson price by 2/3 does not decrease performance in tested settings, while 1/3 is worse across all settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MT pricing instead of Myerson-only or retention-threshold-only pricing | Skip pricing · Simulation instances | revenue relative to the better alternative: within $1\% in 82\% of cases; strictly outperforms the next best option in 12\% of cases | Helped |
| Use retention-threshold-only pricing instead of Myerson-only pricing | Skip pricing · Simulation instances | revenue: over 20\% of the instances | Mixed |
| Offer multiple skip prices based on how much of the task the player completes | Single-skip pricing · Two-block skip pricing example | revenue: 0.46875 -> \approx 0.53; 0.4375 -> \approx 0.53 | Helped |
| Scale the Myerson price by \nicefrac{2}{3} (ablation) | MT pricing · Simulation settings tested | revenue | Helped |
| Scale the Myerson price by \nicefrac{1}{2} (ablation) | MT pricing · Simulation settings tested | revenue | Mixed |
| Scale the Myerson price by \nicefrac{1}{3} (ablation) | MT pricing · Simulation settings tested | revenue | Hurt |
Surprising findings
- Under whale-like type distributions, the utility-optimal and revenue-optimal prices can coincide at high prices, so high prices can give both high utility and high revenue.
- Without distributional assumptions the gap between known-types and unknown-types revenue is unbounded, so a constant-factor gap can be arbitrarily large.
Limitations
- Model assumes single-player types fixed across tasks, myopic players, and i.i.d. retention draws; repeated-task results rely on these assumptions.
- Fully-sensitive results are supported empirically rather than with general theory.
- Simulations use hand-chosen parametric distributions rather than empirical player data.
Experimental setup
Metrics: expected player utility revenue revenue ratio relative to known-types optimum
Baselines: Myerson optimal price only retention threshold pricing independent retention draws variant scaled Myerson pricing
Builds on: Myerson optimal auction / posted pricing conspicuous consumption models monotone hazard rate distributions
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