An efficient mechanism for allocation of a divisible good

We propose an efficient mechanism for allocation of a divisible good. Strategic buyers play a game by submitting bids to the seller. The seller allocates the good in proportion to the bids and charges the buyers nonuniform prices according to the mechanism. Under some mild conditions on the valuation functions of the buyers, there is a unique NEP and the allocation at the NEP is efficient. The prices charged to the buyers at the NEP are bounded above, and can be made arbitrarily close to the market clearing price for price-taking buyers. The relationship to work of Vikrey-Clark-Groves, Johari and Tsitsiklis, and Sanghavi and Hajek is discussed. Index: 1 – Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 – Efficient Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 – Buyers’ Payment and Seller’s Revenue . . . . . . . . . . . . . . . . . . . 11 4 – Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 University of Illinois at Urbana Champaign March 11, 2004 An Efficient Mechanism for Allocation of a Divisible Good 2 1 – Introduction Network Resource Allocation Problem ☞ Divisible goods ☞ Strategic buyers with different valuation functions ☞ Seek a mechanism to promote social efficiency How to characterize “good” use of the network? ☞ Efficiency:What is the aggregate value of the allocation compared to the maximum possible? ☞ Fairness: How is the network value distributed among buyers? University of Illinois at Urbana Champaign March 11, 2004 An Efficient Mechanism for Allocation of a Divisible Good 3 Market with Divisible Goods — Single link case, N buyers, N ≥ 2. Total amount of capacity C is infinitely divisible. Buyer i has strictly concave, strictly increasing and continuously differentiable valuation function Ui(xi) on [0, C]. (U ′ i(0) = ∞ is ok). SYSTEM Problem: