Equilibrium in Combinatorial Public Projects

We study simple item bidding mechanisms for the combinatorial public project problem and explore their efficiency guarantees in various well-known solution concepts. We first study sequential mechanisms where each agent, in sequence, reports her bid for every item in a predefined order on the agents determined by the mechanism. We show that if agents' valuations are unit-demand any subgame perfect equilibrium of a sequential mechanism achieves the optimal social welfare. For the simultaneous bidding equivalent of the above auction we show that for any class of bidder valuations, all Strong Nash Equilibria achieve at least a Ologn factor of the optimal social welfare. For Pure Nash Equilibria we show that the worst-case loss in efficiency is proportional to the number of agents. For public projects in which only one item is selected we show constructively that there always exists a Pure Nash Equilibrium that guarantees at least $\frac{1}{2}1-\frac{1}{n}$ of the optimum. We also show efficiency bounds for Correlated Equilibria and Bayes-Nash Equilibria, via the recent smooth mechanism framework [26].

[1]  Shaddin Dughmi,et al.  A truthful randomized mechanism for combinatorial public projects via convex optimization , 2011, EC '11.

[2]  Renato Paes Leme,et al.  On the efficiency of equilibria in generalized second price auctions , 2011, EC '11.

[3]  Michal Feldman,et al.  Simultaneous auctions are (almost) efficient , 2012, STOC '13.

[4]  Tim Roughgarden,et al.  Welfare guarantees for combinatorial auctions with item bidding , 2011, SODA '11.

[5]  Renato Paes Leme,et al.  GSP auctions with correlated types , 2011, EC '11.

[6]  Uriel Feige,et al.  On maximizing welfare when utility functions are subadditive , 2006, STOC '06.

[7]  David Buchfuhrer,et al.  Computation and incentives in combinatorial public projects , 2010, EC '10.

[8]  Yaron Singer,et al.  Inapproximability of Combinatorial Public Projects , 2008, WINE.

[9]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[10]  Y. Mansour,et al.  4 Learning , Regret minimization , and Equilibria , 2006 .

[11]  Renato Paes Leme,et al.  The curse of simultaneity , 2012, ITCS '12.

[12]  Renato Paes Leme,et al.  Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[13]  Fan Chung Graham,et al.  Internet and Network Economics, Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007, Proceedings , 2007, WINE.

[14]  Vasilis Syrgkanis,et al.  Bayesian Games and the Smoothness Framework , 2012, ArXiv.

[15]  Tim Roughgarden,et al.  The price of anarchy in games of incomplete information , 2012, EC '12.

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

[17]  Allan Borodin,et al.  Price of anarchy for greedy auctions , 2009, SODA '10.

[18]  Drew Fudenberg,et al.  Game theory (3. pr.) , 1991 .

[19]  Y. Mansour,et al.  Algorithmic Game Theory: Learning, Regret Minimization, and Equilibria , 2007 .

[20]  Éva Tardos,et al.  Composable and efficient mechanisms , 2012, STOC '13.

[21]  Tim Roughgarden,et al.  Intrinsic Robustness of the Price of Anarchy , 2015, J. ACM.

[22]  Haim Kaplan,et al.  Non-price equilibria in markets of discrete goods , 2011, EC '11.

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

[24]  Aaron Roth,et al.  Differentially private combinatorial optimization , 2009, SODA '10.

[25]  Sampath Kannan,et al.  The Exponential Mechanism for Social Welfare: Private, Truthful, and Nearly Optimal , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[26]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

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