Adjusting Prices in the Many-to-many Assignment Game
AbstractStarting with an initial price vector, prices are adjusted in order to eliminate the demand excess and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which sellers should those transfers be made (minimal overdemanded sets) is the key definition in the description of the algorithm. Such approach was previously used by several authors. We introduce a novel distinction by considering multiple sellers owing multiple identical objects and multiple buyers with a quota greater than one consuming at most one unit of each seller’s good. This distinction induces a necessarily more complicated construction of the overdemanded sets than the constructions existing in the literature, even in the simplest case of additive utilities considered here. As the previous papers, our mechanism yields the minimum competitive equilibrium price vector. A procedure to find the maximum competitive equilibrium price vector is also provided.
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Bibliographic InfoPaper provided by Brown University, Department of Economics in its series Working Papers with number 2008-12.
Date of creation: 2008
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Postal: Department of Economics, Brown University, Providence, RI 02912
matching; stable payoff; competitive equilibrium payoff; optimal stable payoff; lattice social costs; pure comparative vigilance; super-symmetric rule;
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- Fagebaume, Alexis & Gale, David & Sotomayor, Marilda, 2010. "A note on the multiple partners assignment game," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 388-392, July.
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