Abstract
We provide a quantitative boundary on the stepsizes of bid and ask of a double auction (DA) mechanism to answer two questions, when the DA mechanism is efficient and when it creates bubbles and crashes. The main result is that the ratio of the two stepsizes and their spread are the key factors for the DA mechanism to be efficient. Sentiment that leads to a swing in the spread and the ratio of the two stepsizes can result in prices to deviate from the intrinsic value equilibrium. These results are derived from a theoretical analysis of the DA mechanism built on the incremental subgradient method in Nedic and Bertsekas (2001).
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