A Characterization of n-Player Strongly Monotone Scheduling Mechanisms

Our work deals with the important problem of globally characterizing truthful mechanisms where players have multi-parameter, additive valuations, like scheduling unrelated machines or additive combinatorial auctions. Very few mechanisms are known for these settings and the question is: Can we prove that no other truthful mechanisms exist? We characterize truthful mechanisms for n players and 2 tasks or items, as either task-independent, or a player-grouping minimizer, a new class of mechanisms we discover, which generalizes affine minimizers. We assume decisiveness, strong monotonicity and that the truthful payments are continuous functions of players' bids.

[1]  D. Mishra,et al.  Deterministic Single Object Auctions with Private Values , 2012 .

[2]  Shahar Dobzinski,et al.  On characterizations of truthful mechanisms for combinatorial auctions and scheduling , 2008, EC '08.

[3]  Ian A. Kash,et al.  General Truthfulness Characterizations Via Convex Analysis , 2012, WINE.

[4]  Noam Nisan,et al.  Towards a characterization of truthful combinatorial auctions , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[5]  Itai Ashlagi,et al.  Characterizing Vickrey allocation rule by anonymity , 2011, Soc. Choice Welf..

[6]  A. Roth,et al.  Games and Economic Behavior , 1995 .

[7]  Leah Epstein,et al.  A Unified Approach to Truthful Scheduling on Related Machines , 2012, Math. Oper. Res..

[8]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

[9]  Robert M Thrall,et al.  Mathematics of Operations Research. , 1978 .

[10]  M. André.  Arrow (Kenneth) - Social Choice and Individual Values , 1953 .

[11]  Michael E. Saks,et al.  Weak monotonicity suffices for truthfulness on convex domains , 2005, EC '05.

[12]  J. Rochet.  A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

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

[14]  Ron Lavi,et al.  Searching for the possibility: impossibility border of truthful mechanism design , 2007, SECO.

[15]  Angelina Vidali,et al.  The Geometry of Truthfulness , 2009, WINE.

[16]  Elias Koutsoupias,et al.  A characterization of 2-player mechanisms for scheduling , 2008, ESA.

[17]  Robert D. Kleinberg,et al.  Truthful germs are contagious: A local-to-global characterization of truthfulness , 2014, Games Econ. Behav..

[18]  Leah Epstein,et al.  A unified approach to truthful scheduling on related machines , 2013, SODA.

[19]  Ahuva Mu'alem,et al.  Setting lower bounds on truthfulness: extended abstract , 2007, SODA.

[20]  Elias Koutsoupias,et al.  A Lower Bound of 1+phi for Truthful Scheduling Mechanisms , 2007, MFCS.

[21]  Noam Nisan,et al.  Multi-unit auctions: beyond roberts , 2010, EC '11.

[22]  Noam Nisan,et al.  Algorithmic Mechanism Design , 2001, Games Econ. Behav..

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

[24]  Itai Ashlagi,et al.  Optimal Lower Bounds for Anonymous Scheduling Mechanisms , 2012, Math. Oper. Res..

[25]  Rudolf Müller,et al.  Dominant Strategy Mechanisms with Multidimensional Types , 2005, Computing and Markets.

[26]  Annamária Kovács,et al.  A Global Characterization of Envy-Free Truthful Scheduling of Two Tasks , 2011, WINE.

[27]  Noam Nisan,et al.  Two simplified proofs for Roberts’ theorem , 2009, Soc. Choice Welf..

[28]  Elias Koutsoupias,et al.  A Lower Bound for Scheduling Mechanisms , 2007, SODA '07.