Congestion games model shared resources where each player's cost depends on how many others choose the same resource — roads, servers, parking spots. The standard fix for inefficient equilibria is tolling: charge players for using congested resources. But monetary tolls are regressive — they burden low-income players more, achieving efficiency at the cost of fairness.
This paper replaces money with tokens. Players receive a fixed budget of non-transferable tokens that they spend to access resources. The tokens have no external value; they are purely an allocation mechanism. When your tokens run out, you wait. When others' tokens run out, resources free up.
The key result is that integer-valued token tolls exist in closed form that provably steer the aggregate dynamics toward an allocation that is simultaneously efficient and fair. The mechanism works for boundedly rational players using a mean-field approximation — it does not require full rationality or common knowledge of the game's structure.
The fairness guarantee is built into the design: because everyone receives the same token budget and tokens have no market value, wealth differences cannot translate into access differences. A rich player and a poor player have the same purchasing power in the token economy. The tolls shape behavior through budgeting constraints, not willingness to pay.
The convergence is from any initial condition: regardless of how players start, the token dynamics guide them toward the efficient-fair allocation. The mechanism is self-correcting because overspending depletes your budget, automatically reducing your future demand. The scarcity is artificial but the behavioral effect is real.