Bayesian Budget Feasibility with Posted Pricing

We consider the problem of budget feasible mechanism design proposed by Singer, but in a Bayesian setting. A principal has a public value for hiring a subset of the agents and a budget, while the agents have private costs for being hired. We consider both additive and submodular value functions of the principal. We show that there are simple, practical, ex post budget balanced posted pricing mechanisms that approximate the value obtained by the Bayesian optimal mechanism that is budget balanced only in expectation. A main motivating application for this work is crowdsourcing, e.g., on Mechanical Turk, where workers are drawn from a large population and posted pricing is standard. Our analysis methods relate to contention resolution schemes in submodular optimization of Vondràk et al. and the correlation gap analysis of Yan.

[1]  Jan Vondrák,et al.  Maximizing a Monotone Submodular Function Subject to a Matroid Constraint , 2011, SIAM J. Comput..

[2]  Balasubramanian Sivan,et al.  Optimal Crowdsourcing Contests , 2011, Encyclopedia of Algorithms.

[3]  Saeed Alaei,et al.  Bayesian Combinatorial Auctions: Expanding Single Buyer Mechanisms to Many Buyers , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[4]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[5]  Ludwig Ensthaler,et al.  Bayesian Optimal Knapsack Procurement , 2013, Eur. J. Oper. Res..

[6]  Andreas Krause,et al.  Truthful incentives in crowdsourcing tasks using regret minimization mechanisms , 2013, WWW.

[7]  Robert D. Kleinberg,et al.  Learning on a budget: posted price mechanisms for online procurement , 2012, EC '12.

[8]  Aleksandrs Slivkins,et al.  Incentivizing High Quality Crowdwork , 2015 .

[9]  Maxim Sviridenko,et al.  A note on maximizing a submodular set function subject to a knapsack constraint , 2004, Oper. Res. Lett..

[10]  Nikhil R. Devanur,et al.  Prior-free auctions for budgeted agents , 2012, EC '13.

[11]  Jason D. Hartline,et al.  Multi-parameter mechanism design and sequential posted pricing , 2009, STOC '10.

[12]  Amin Saberi,et al.  Correlation robust stochastic optimization , 2009, SODA '10.

[13]  Aravind Srinivasan,et al.  On k-Column Sparse Packing Programs , 2009, IPCO.

[14]  Samir Khuller,et al.  The Budgeted Maximum Coverage Problem , 1999, Inf. Process. Lett..

[15]  Yaron Singer,et al.  Budget Feasible Mechanisms , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[16]  Shuchi Chawla,et al.  Multi-parameter mechanism design and sequential posted pricing , 2010, BQGT.

[17]  Qiqi Yan,et al.  Mechanism design via correlation gap , 2010, SODA '11.

[18]  Péter Esö,et al.  Auction design with a risk averse seller , 1999 .

[19]  Nicole Immorlica,et al.  Social Status and Badge Design , 2015, WWW.

[20]  Gagan Goel,et al.  Mechanism Design for Crowdsourcing: An Optimal 1-1/e Competitive Budget-Feasible Mechanism for Large Markets , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[21]  Chandra Chekuri,et al.  Submodular function maximization via the multilinear relaxation and contention resolution schemes , 2011, STOC '11.

[22]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[23]  Ning Chen,et al.  Budget feasible mechanism design: from prior-free to bayesian , 2012, STOC '12.

[24]  Ning Chen,et al.  On the approximability of budget feasible mechanisms , 2010, SODA '11.

[25]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[26]  Jeremy I. Bulow,et al.  The Simple Economics of Optimal Auctions , 1989, Journal of Political Economy.

[27]  Jan Vondrák,et al.  Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract) , 2007, IPCO.

[28]  Yaron Singer,et al.  Pricing mechanisms for crowdsourcing markets , 2013, WWW.