Auction Mechanics

We augment the standard uniform price auction with two features that create a robust and competitive market:

1. Elastic Supply Schedule: We adjust supply based on price. Low prices trigger limited supply to prevent undervaluation.
2. Alternative Tie-Breaking Rule: Our tie-breaking rule handles excess demand by creating pressure at the marginal quantity level.

The supply curve starts concave and becomes constant at maximum capacity. This design prevents dramatic underpricing. We parameterize the supply function as:

S(p) = ap^n

Here, 'a' and 'n' are constants. We calculate price p' by setting the maximum quantity: q_max = ap^n.

Bidders submit multiple (quantity, price) pairs to express their demand function. The auction aggregates all demands and matches them to supply to find the market-clearing price.

When demand exceeds supply, we allocate shares based on individual demand at that point. This approach incentivizes bidders to reveal true valuations and prevents low-price equilibria.