Fair Congested Assignment

We must assign n agents to m posts subject to negative congestion; what assignment is fair and efficient? If congestion is anonymous (each agent adds one unit), it is always possible to assign each agent to one of the agent’s top n out of the [Formula: see text] feasible allocations. This ordinal interpretation of ex ante fairness can be adjusted if congestion is weighted (agent-specific). An assignment is competitive if I don’t want to move to an empty post or to an occupied one at its current congestion level. If it exists, the competitive assignment is essentially unique, efficient, and ex ante fair. Among agents endowed with cardinal expected utilities, we can randomize the selection of our assignment. Under anonymous congestion, every problem has a unique competitive congestion profile implemented by a mixture of deterministic assignments, rounding up or down the competitive congestion, and approximately ex ante fair, efficient, and welfare equivalent. Some of these properties are lost under weighted congestion.