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aggregate allocation is efficient characterize commodities conditional distribution context contingency correlation criterion depends Design of Efficient direct revelation game Divergence Theorem Double Auctions Econometrica Economic Theory efficient allocation Efficient Trading Procedures ensure Envelope Theorem ex ante efficiency ex post participation feasible decision rule formulation Guesnerie and Laffont Holmstrom implementation incentive compatibility incentive constraints incentive efficient individual rationality constraints Interim efficiency Jacobian Journal of Economic Kennan and Wilson Lagrange Multipliers maximize McAfee mechanism design member's type member's utility Milgrom Mirrlees 1976a Moral Hazard multiplier Myerson and Satterthwaite necessary conditions nonlinear pricing problem number of traders obtained optimal allocation outcome Zj Pareto criterion participant's payment rule Pi(U post participation constraint principal-agent Principal-Agent Problems private information Ramsey number random variable reported types revelation principle revenue requirement Robert Wilson rule is incentive Satterthwaite 1983 sellers sharing rule specified Theorem transversality condition truthful reporting type-contingent Ui(U virtual utilities welfare weights