Satterthwaite, Mark, Williams, Steven R. and Zachariadis, Konstantinos (2012) Price discovery. . (Unpublished)
Within a novel model of correlated private values (CPV) we investigate how well a particular market mechanism, the buyer's bid double auction (BBDA), performs in small and moderate sized markets: do well behaved equilibria exist and is there rapid convergence to efficient allocations and prices that accurately identify the market's underlying state. We bound traders' strategic behavior, as a function of market size, and prove rates of convergence to zero of (i) the allocation's inefficiency and (ii) the error in estimating the market's underlying state. These rates imply that even in moderate sized markets strategic behavior has an inconsequential effect on the estimate of the market state. We also show that the affiliation condition on traders' values and costs familiar from auction theory does not imply affiliation of bids and offers and therefore does not play the same pivotal role as it plays in auction theory in proving existence. Using a combination of theorems and numerical experiments we establish that simple offset equilibria do exist even in small markets, despite the failure of affiliation between bids and offers. Furthermore, an asymptotic analysis provides a simple formula for approximately optimal bidding in any size market for a particular instance of the model. We extend our model to the case of correlated interdependent values (CIV). While we have been unable to obtain the same sequence of results as we have secured in the CPV case, we do show that the structure of equilibria in the CIV case is unchanged. As a consequence we can straightforwardly compute a substantial sample of equilibria for different market sizes and show that the BBDA's convergence properties do not change qualitatively with the introduction of interdependence.
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