The Effects of Latency on a Progressive Second-Price Auction

TL;DR

This study examines how latency, asynchronicity, and randomness in initial bids affect $\a{\varepsilon}$-Nash equilibria in Lazar and Semret's progressive second-price auction for a divisible resource. It introduces an algorithm to construct zero- and minimal-revenue $\varepsilon$-Nash equilibria and models latency with Weibull renewal processes to assess convergence and outcome stability under delays. A key finding is that a reserve price just below the clearing price stabilizes seller revenue without harming efficiency, and that convergence of truthful $\varepsilon$-best replies persists under substantial latency, with individual utilities remaining predictable under elastic demand. The results provide practical guidance for designing robust, decentralized real-time auctions, highlighting reserve pricing and the resilience of equilibrium outcomes to timing and initialization randomness.

Abstract

The progressive second-price auction of Lazar and Semret is a decentralized mechanism for the allocation and real-time pricing of a divisible resource. Our focus is on how delays in the receipt of bid messages, asynchronous analysis by buyers of the market and randomness in the initial bids affect the $\varepsilon$-Nash equilibria obtained by the method of truthful $\varepsilon$-best reply. We introduce an algorithm for finding minimal-revenue equilibrium states and then show that setting a reserve price just below clearing stabilizes seller revenue while maintaining efficiency. Utility is of primary interest given the assumption of elastic demand. Although some buyers experienced unpredictability in the value and cost of their individual allocations, their respective utilities were predictable.

Figures (3)

• Figure 1: Comparison of the probability density functions governing the time between evaluation of bids and the communication latency to transmit a bid to the auction.
• Figure 2: Left shows that changing the scale $\lambda_{\rm c}$ of the communication latency has minimal effect on the ensemble-averaged price and total utility received by all buyers. Right shows the average value and cost for each individual buyer when $\lambda_c=1$.
• Figure 3: The outcomes for lazy buyers who evaluate the market 17 times less frequently and experience 17 times the latency in their bid messages compared to an equal number of industrious buyers with identical valuations.

Theorems & Definitions (8)

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