Large Market Games with Near Optimal Efficiency
Richard Cole, Yixin Tao

TL;DR
This paper investigates how the efficiency of large markets improves with size under strategic behavior, showing that the Price of Anarchy approaches 1 in large Walrasian auctions and Fisher markets with certain conditions.
Contribution
It proves that in large markets with specific assumptions, the Price of Anarchy approaches optimal efficiency, providing quantitative bounds on the tradeoff between market size and efficiency.
Findings
PoA tends to 1 as market size increases in large Walrasian auctions.
PoA tends to 1 in large Fisher markets with homogeneous monotone utilities.
Market size and demand uncertainty are key factors in efficiency improvements.
Abstract
As is well known, many classes of markets have efficient equilibria, but this depends on agents being non-strategic, i.e. that they declare their true demands when offered goods at particular prices, or in other words, that they are price-takers. An important question is how much the equilibria degrade in the face of strategic behavior, i.e. what is the Price of Anarchy (PoA) of the market viewed as a mechanism? Often, PoA bounds are modest constants such as 4/3 or 2. Nonetheless, in practice a guarantee that no more than 25% or 50% of the economic value is lost may be unappealing. This paper asks whether significantly better bounds are possible under plausible assumptions. In particular, we look at how these worst case guarantees improve in the following large settings. Large Walrasian auctions: These are auctions with many copies of each item and many agents. We show that the PoA…
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Taxonomy
TopicsGame Theory and Applications · Auction Theory and Applications · Economic theories and models
