Optimal trading mechanisms with ex ante unidentified traders.

*(English)*Zbl 0994.91043The paper considers the problem of designing a rule to determine the terms of trade among several traders who own some units of a good to be traded and have private information about their valuation of objects. In the paper, it is assumed that any trader may be sated at consumption levels below the economy wide endowment. As a consequence, a trader holding some units of the good that are less than his/her sated consumption level may be either a seller or a buyer depending on the realisation of his/her privately observed information and his/her choice of the trading mechanism. In other words, the role of a trader as a buyer or a seller is endogenously determined by his/her bids but cannot be identified prior to trade. The paper presents first the format structure of the multilateral trading problem, followed by a general characterisation of all incentive, compactible and individually rational mechanisms. The way to construct the trading mechanism that maximises a weighted sum of expected total gains from trade and expected proftit to the market maker is presented then. This optimal mechanism is shown to characterise the ex ante efficient mechanism for some particular weight, and to converge to a bid-ask mechanism when the number of traders in the economy becomes large.

Reviewer: Vangelis Grigoroudis (Chania)

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\textit{H. Lu} and \textit{J. Robert}, J. Econ. Theory 97, No. 1, 50--80 (2001; Zbl 0994.91043)

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##### References:

[1] | Chatterjee, K.; Samuelson, W., Bargaining under incomplete information, Oper. res., 31, 835-851, (1983) · Zbl 0537.90102 |

[2] | Cramton, P.; Gibbons, R.; Klemperer, P., Dissolving a partnership efficiently, Econometrica, 55, 615-632, (1987) · Zbl 0632.90097 |

[3] | Gresik, T.; Satterthwaite, M., The rate at which a simple market becomes efficient as the number of traders increases: an asymptotic result for optimal trading mechanisms, J. econ. theory, 48, 304-332, (1989) · Zbl 0673.90016 |

[4] | HolmstrĂ¶m, B.; Myerson, R.B., Efficient and durable decision rules with incomplete information, Econometrica, 51, 1799-1820, (1983) · Zbl 0521.90008 |

[5] | Laffont, J.-J.; Tirole, J., A theory of incentives in procurement and regulation, (1993), The MIT Press Cambridge |

[6] | Laffont, J.-J.; Maskin, E.; Rochet, J.-C., Optimal non-linear pricing with two dimensional characteristics, () |

[7] | Leininger, W.; Linhart, P.B.; Radner, R., Equilibria of the sealed-bid mechanism for bargaining with incomplete information, J. econ. theory, 48, 63-106, (1989) · Zbl 0669.90099 |

[8] | Lu, H., Efficient performance in a simple market with incomplete information, (1999), University of Ottawa |

[9] | Makowski, L.; Mezzetti, C., The possibility of efficient mechanisms for trading an indivisible object, J. econ. theory, 59, 451-465, (1993) · Zbl 0771.90022 |

[10] | Maskin, E.S.; Riley, J.G., Optimal multi-unit auctions, () |

[11] | McAfee, R.P., Efficient allocation with continuous quantities, J. econ. theory, 53, 51-74, (1991) · Zbl 0742.90028 |

[12] | Mussa, M.; Rosen, S., Monopoly and product quality, J. econ. theory, 18, 301-317, (1987) · Zbl 0403.90007 |

[13] | Myerson, R.B., Incentive compatibility and the bargaining problem, Econometrica, 47, 61-73, (1979) · Zbl 0399.90008 |

[14] | Myerson, R.B., Optimal auction design, Math. oper. res., 6, 58-73, (1981) · Zbl 0496.90099 |

[15] | Myerson, R.B.; Satterthwaite, M., Efficient mechanisms for bilateral trading, J. econ. theory, 28, 265-281, (1983) · Zbl 0523.90099 |

[16] | Rochet, J.-C.; Chone, P., Ironing, sweeping and multidimensional screening, Econometrica, 66, 783-826, (1998) · Zbl 1015.91515 |

[17] | Rustichini, A.; Satterthwaite, M.A.; Williams, S.R., Convergence to efficiency in a simple market with incomplete information, Econometrica, 62, 1041-1063, (1994) · Zbl 0820.90031 |

[18] | Satterthwaite, M.; Williams, S.R., Bilateral trade with the sealed-bid k-double auction: existence and efficiency, J. econ. theory, 48, 107-133, (1989) · Zbl 0672.90014 |

[19] | Spulber, D., Bargaining and regulation with asymmetric information about demand and supply, J. econ. theory, 44, 251-268, (1988) · Zbl 0664.90101 |

[20] | Williams, S.R., Efficient performance in two-agent bargaining, J. econ. theory, 41, 154-172, (1987) · Zbl 0627.90010 |

[21] | Wilson, R., Incentive efficiency of double auctions, Econometrica, 53, 1101-1115, (1985) · Zbl 0584.90013 |

[22] | Wilson, R., Efficient trading, () |

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