On the Strategy-Proof and Smooth Allocation of Private Goods in Production Economies

We consider the problem of allocating private goods in a production economy, which is an economy where the total consumption bundle must lie on some smooth manifold in < m +. We describe a family of social choice functions called generalized serial mechanisms which have the extremely strong strategic property that (1) a utility proole is a Nash equilibrium if and only if the proole produces the truthful outcome, and (2) every Nash equilibrium is a strict strong equilibrium (i.e., at least one member in every deviating coalition that perturbs the outcome must be strictly less well oo). We then introduce certain smoothness (diierentiability) conditions and show that any anonymous, nonconstant, and smooth social choice function which is coalitionally strategy-proof, or is strategy-proof and nonbossy, must be a generalized serial mechanism. This work is an outgrowth of Moulin-Shenker (1991) which discusses the serial cost sharing method. This work also relies heavily on the result of Satterthwaite and Sonnenschein (1981) which states that a nonbossy and strategy-proof social choice function must be acyclic at every diierentiable point. Please do not circulate or quote!