Auction Mechanics

The standard uniform price auction is augmented with two key features to create a more robust and competitive market:

1. Elastic Supply Schedule: Instead of a fixed supply, we offer an elastic supply. If the price is very low, we offer a limited amount of options.
2. Alternative Tie-Breaking Rule: We introduce a different tie-breaking rule for excess demand to create more pressure at the marginal quantity level.

The supply curve is designed to be initially concave and then constant at the maximum capacity. This approach helps to mitigate the risk of dramatic underpricing. The supply function is parameterized as follows:

S(p) = ap^n

Where 'a' and 'n' are constants. The price p' is calculated by setting the max quantity, q_max = ap^n.

Each bidder can submit several (quantity, price) pairs, which allows us to elicit their partial demand function. The auction proceeds by aggregating the demand and matching it to the supply to determine a market-clearing price.

In the case of excess demand, we use an alternative allocation rule that gives a share relative to the individual demand at that point. This creates stronger incentives for bidders to bid closer to their true valuations and reduces the tendency to end up in a low-price equilibrium.