How efficient are pay-as-bid auction games?
How competitive are pay-as-bid auction games?
This paper analyzes "pay-as-bid" auction games, where participants submit supply functions (how much they'll sell at each price), and are paid their bid price for the quantity sold at market clearing. Traditional supply function models often assume a uniform clearing price. This research focuses on discriminatory pricing and varying costs among participants.
For LLM-based multi-agent systems, a key takeaway is the strategic complexity introduced by pay-as-bid auctions. The choice of supply function dramatically influences outcomes. The paper establishes that if participants can submit any continuous, non-decreasing supply function, Nash equilibria (stable strategy profiles) often don't exist. However, restricting strategies to Lipschitz continuous functions guarantees the existence of equilibria, which have a simple, piecewise-linear form. This simplified structure could potentially be leveraged for agent design in LLM-based multi-agent systems interacting in market-like environments. Furthermore, under certain conditions (affine demand, homogeneous marginal costs at zero production), the pay-as-bid auction leads to a unique outcome up to the clearing price, potentially simplifying agent reasoning and learning. The paper's insights into how restricting the strategy space can lead to well-behaved outcomes are relevant to LLM-based systems where enforcing or incentivizing certain agent behaviors might be crucial for stability and efficiency.