Abstract
When traders have private information about a common value good, adverse selection alone is insufficient to prevent trade of the good and estimation of the common value based upon the traders’ private information. We explore sufficient conditions for nonexistence of trading mechanisms in which trade of a common good occurs, along with cases in which such mechanisms exist.
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Notes
The use of “ex post” here is consistent with its definition as “based on or determined by actual results, rather than expectations; calculated retrospectively” (OED Online, accessed Sept. 2021, Oxford University Press). I emphasize the phrase “actual results”: here, this means the information that the mechanism actually provides to a trader, which may be incomplete.
It is worth emphasizing that the Revelation Principle does not assert the “informational equivalence” of any equilibrium of any game with the “honest” equilibrium of a complete information direct mechanism.
Throughout this paper, the arguments of expected utility \(U_{i}(\cdot ;\cdot )\) are separated by a semi-colon, with the arguments before the semi-colon representing signals that are known by trader i at the time of the calculation and the argument after the semi-colon representing the announced signal of trader i.
The possibility results in Cramton et al. (1987, Prop. 1) and here are similar in that a partner may either buy or sell. Trading on either side of the market plays a different role, however, in these two results. Having a partner both buy and sell directly ensures incentive compatibility in (31) above. In contrast, in Cramton et al. (1987, Prop. 1), it changes the welfare of the “worst-off” type of each partner and therefore affects the potential to tax the partners and fund the deficit incurred from satisfying incentive compatibilty. This is explained in Williams (1999, sec. 2.3) and is captured by ineq. (1) in Cramton et al. (1987, p. 618). It also applies to McAfee (1992, p. 56, ineq. (10)), which studies efficient allocation in bilateral bargaining when each trader can either buy or sell.
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Acknowledgements
I thank Georgy Artemov, Ivan Balbuzanov, Aaron Barkley, David Byrne, Simon Loertscher, Alex Nichifor, Kostas Zachariadis, Moritz Meyer-ter-Vehn and the referees of this paper for their comments.
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Williams, S.R. Trade of a common value good. Rev Econ Design 27, 701–724 (2023). https://doi.org/10.1007/s10058-022-00322-6
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DOI: https://doi.org/10.1007/s10058-022-00322-6