Combinatorial Walrasian Equilibrium

We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian equilibrium (WE), which provides a simple and transparent pricing structure that achieves optimal social welfare. The main weakness of the WE notion is that it exists only in very restrictive cases. To overcome this limitation, we introduce the notion of a combinatorial Walrasian equilibium (CWE), a natural relaxation of WE. The difference between a CWE and a (noncombinatorial) WE is that the seller can package the items into indivisible bundles prior to sale, and the market does not necessarily clear. We show that every valuation profile admits a CWE that obtains at least half the optimal (unconstrained) social welfare. Moreover, we devise a polynomial time algorithm that, given an arbitrary allocation, computes a CWE that achieves at least half its welfare. Thus, the economic ...

[1]  Faruk Gul,et al.  WALRASIAN EQUILIBRIUM WITH GROSS SUBSTITUTES , 1999 .

[2]  Edith Cohen,et al.  Envy-Free Makespan Approximation , 2009, SIAM J. Comput..

[3]  Uriel Feige,et al.  Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[4]  L. Shapley,et al.  The assignment game I: The core , 1971 .

[5]  D. Foley.  Resource allocation and the public sector , 1967 .

[6]  Vahab S. Mirrokni,et al.  Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions , 2008, EC '08.

[7]  Noam Nisan,et al.  On the Computational Power of Demand Queries , 2009, SIAM J. Comput..

[8]  Shuchi Chawla,et al.  Bayesian algorithmic mechanism design , 2014, SECO.

[9]  Yoav Shoham,et al.  Truth revelation in approximately efficient combinatorial auctions , 2002, EC '99.

[10]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[11]  S. Bikhchandani,et al.  Competitive Equilibrium in an Exchange Economy with Indivisibilities , 1997 .

[12]  Shahar Dobzinski,et al.  Optimization with demand oracles , 2012, EC '12.

[13]  Jason D. Hartline,et al.  Envy, truth, and profit , 2011, EC '11.

[14]  Sushil Bikhchandani,et al.  The Package Assignment Model , 2002, J. Econ. Theory.

[15]  Chaitanya Swamy,et al.  Approximation Algorithms for Single-minded Envy-free Profit-maximization Problems with Limited Supply , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[16]  H. Varian.  Equity, Envy and Efficiency , 1974 .

[17]  Robert D. Kleinberg,et al.  Bayesian incentive compatibility via matchings , 2011, SODA '11.

[18]  H. Leonard.  Elicitation of Honest Preferences for the Assignment of Individuals to Positions , 1983, Journal of Political Economy.

[19]  Moshe Babaioff.  Truthful Mechanisms for One-Parameter Agents , 2016, Encyclopedia of Algorithms.

[20]  Moshe Tennenholtz,et al.  Bundling equilibrium in combinatorial auctions , 2002, Games Econ. Behav..

[21]  Christos H. Papadimitriou,et al.  On the Hardness of Being Truthful , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[22]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[23]  Hu Fu,et al.  Conditional equilibrium outcomes via ascending price processes with applications to combinatorial auctions with item bidding , 2012, EC '12.

[24]  Ahuva Mu'alem,et al.  On Multi-dimensional Envy-Free Mechanisms , 2009, ADT.

[25]  Lawrence M. Ausubel,et al.  Ascending Auctions with Package Bidding , 2002 .

[26]  Amos Fiat,et al.  Envy, Multi Envy, and Revenue Maximization , 2009, WINE.

[27]  Venkatesan Guruswami,et al.  On profit-maximizing envy-free pricing , 2005, SODA '05.

[28]  David C. Parkes,et al.  Iterative Combinatorial Auctions: Theory and Practice , 2000, AAAI/IAAI.

[29]  Noam Nisan,et al.  Truthful randomized mechanisms for combinatorial auctions , 2006, STOC '06.

[30]  Noam Nisan,et al.  Informational limitations of ascending combinatorial auctions , 2010, J. Econ. Theory.

[31]  R. Aumann.  Values of Markets with a Continuum of Traders , 1975 .

[32]  Patrick Briest.  Towards Hardness of Envy-Free Pricing , 2006, Electron. Colloquium Comput. Complex..

[33]  Michael P. Wellman,et al.  AkBA: a progressive, anonymous-price combinatorial auction , 2000, EC '00.

[34]  Tim Roughgarden,et al.  Truthful Approximation Schemes for Single-Parameter Agents , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.