We study the repeated allocation of a single indivisible resource among $n$ strategic players. Each player $i$ has a privately known value distribution $D_i$, and values are drawn independently across players and periods. The goal is to find fair and efficient mechanisms. We apply the repeated first-price auction with equal initial endowments of virtual money. We show that each player can asymptotically secure the same fair-floor guarantee $f(D_i)$ as in Csóka 2026; consequently, the mechanism is $1.283$-optimal. This provides a simpler and more robust alternative mechanism for this special case and may also help derive sharper upper bounds on the price of anarchy.

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