Strategy-Proofness in the Large

We propose a criterion of approximate incentive compatibility, strategy-proofness in the large (SP-L), and argue that it is a useful second-best to exact strategy-proofness (SP) for market design. Conceptually, SP-L requires that an agent who regards a mechanism’s “prices” as exogenous to her report—be they traditional prices as in an auction mechanism, or price-like statistics in an assignment or matching mechanism—has a dominant strategy to report truthfully. Mathematically, SP-L weakens SP in two ways: (1) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (2) incentive compatibility is evaluated ex interim, with respect to all full-support i.i.d. probability distributions of play, rather than ex post with respect to all possible realizations of play. This places SP-L in between the traditional notion of approximate SP, which evaluates incentives to manipulate ex post and as a result is too strong to obtain our main results in support of SP-L, and the traditional notion of approximate Bayes-Nash incentive compatibility, which, like SP-L, evaluates incentives to manipulate ex interim, but which imposes common knowledge and strategic sophistication assumptions that are often viewed as unrealistic.

[1]  Adam J. Kapor,et al.  NBER WORKING PAPER SERIES HETEROGENEOUS BELIEFS AND SCHOOL CHOICE MECHANISMS , 2019 .

[2]  Paul R. Milgrom,et al.  Designing Random Allocation Mechanisms: Theory and Applications , 2013 .

[3]  T. Bewley.  Advances in Economic Theory: Fifth World Congress , 2009 .

[4]  Herbert E. Scarf,et al.  A LIMIT THEOREM ON THE CORE OF AN ECONOMY , 1963, Classics in Game Theory.

[5]  E. Kalai.  Large Robust Games , 2004 .

[6]  Parag A. Pathak,et al.  Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match , 2009 .

[7]  Steven R. Williams,et al.  Convergence to Efficiency in a Simple Market with Incomplete Information , 1994 .

[8]  David C. Parkes,et al.  Achieving Budget-Balance with Vickrey-Based Payment Schemes in Exchanges , 2001, IJCAI.

[9]  P. Hammond,et al.  Asymptotically strategy-proof Walrasian exchange , 1998 .

[10]  C. d'Aspremont,et al.  Ordinal Bayesian incentive compatible representations of committees , 1988 .

[11]  K. Arrow.  Social Choice and Individual Values , 1951 .

[12]  R. Radner,et al.  Decision and Organization. A Volume in Honor of Jacob Marschak. Edited by C.B. Mc Guire and Roy Radner. Studies in Mathematical and Managerial Economics, volume 12. Amsterdam, London, North-Holland Publishing Company, 1972 X p. 361 p., fl. 63.00. , 1973, Recherches économiques de Louvain.

[13]  Caterina Calsamiglia,et al.  Structural Estimation of a Model of School Choices: The Boston Mechanism versus Its Alternatives , 2018, Journal of Political Economy.

[14]  Orly Sade,et al.  Sovereign Debt Auctions: Uniform or Discriminatory? , 2009 .

[15]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[16]  A. Roth,et al.  New physicians: a natural experiment in market organization , 1990, Science.

[17]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[18]  R. Zeckhauser,et al.  The Efficient Allocation of Individuals to Positions , 1979, Journal of Political Economy.

[19]  James Schummer,et al.  Almost-dominant strategy implementation: exchange economies , 2004, Games Econ. Behav..

[20]  Leszek Gasieniec,et al.  Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms , 2007, SODA 2007.

[21]  Arunava Sen,et al.  VIRTUAL IMPLEMENTATION IN NASH EQUILIBRIUM , 1991 .

[22]  Judd B. Kessler,et al.  Bringing Real Market Participants' Real Preferences into the Lab: An Experiment that Changed the Course Allocation Mechanism at Wharton , 2016 .

[23]  Lawrence M. Ausubel,et al.  Demand Reduction and Inefficiency in Multi-Unit Auctions , 2014 .

[24]  M. Utku Ünver,et al.  Course Bidding at Business Schools , 2007 .

[25]  Avinatan Hassidim,et al.  "Strategic" Behavior in a Strategy-proof Environment , 2016, EC.

[26]  Itai Ashlagi,et al.  Stability in Large Matching Markets with Complementarities , 2014, Oper. Res..

[27]  Eric Maskin,et al.  Chapter 5 Implementation theory , 2002 .

[28]  M. Friedman,et al.  A Program for Monetary Stability. , 1962 .

[29]  Lawrence M. Ausubel,et al.  The Lovely but Lonely Vickrey Auction , 2004 .

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

[31]  Hitoshi Matsushima,et al.  Virtual implementation in iteratively undominated strategies: complete information , 1992 .

[32]  Shengwu Li.  Obviously Strategy-Proof Mechanisms , 2017 .

[33]  Atila Abdulkadiroglu,et al.  School Choice: A Mechanism Design Approach , 2003 .

[34]  T. Palfrey,et al.  Implementation with Incomplete Information in Exchange Economies , 1989 .

[35]  Nicole Immorlica,et al.  Marriage, honesty, and stability , 2005, SODA '05.

[36]  Alexander Kovalenkov,et al.  Simple Strategy-Proof Approximately Walrasian Mechanisms , 2002, J. Econ. Theory.

[37]  Eric Budish,et al.  The Multi-Unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard , 2010 .

[38]  Hitoshi Matsushima.  A new approach to the implementation problem , 1988 .

[39]  Yeon-Koo Che,et al.  Resolving Conflicting Preferences in School Choice: The 'Boston' Mechanism Reconsidered , 2009 .

[40]  Andrew Postlewaite,et al.  Implementation in differential information economies , 1986 .

[41]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[42]  A. Roth.  A natural experiment in the organization of entry-level labor markets: regional markets for new physicians and surgeons in the United Kingdom. , 1991, The American economic review.

[43]  Guy Laroque,et al.  Fair allocations in large economies , 1981 .

[44]  Aytek Erdil,et al.  A New Payment Rule for Core-Selecting Package Auctions , 2009 .

[45]  E. Maskin.  Nash Equilibrium and Welfare Optimality , 1999 .

[46]  H. Oosterbeek,et al.  The Performance of School Assignment Mechanisms in Practice , 2015, Journal of Political Economy.

[47]  Parag A. Pathak,et al.  Matching with Couples: Stability and Incentives in Large Markets , 2010 .

[48]  Judd B. Kessler,et al.  Changing the Course Allocation Mechanism at Wharton , 2014 .

[49]  Patrick Harless.  A School Choice Compromise: Between Immediate and Deferred Acceptance , 2014 .

[50]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[51]  Andrew V. Goldberg,et al.  Competitive auctions and digital goods , 2001, SODA '01.

[52]  Rann Smorodinsky,et al.  Pivotal Players and the Characterization of Influence , 2000, J. Econ. Theory.

[53]  A. Roth.  What Have We Learned from Market Design? , 2008 .

[54]  P. Pathak,et al.  The Welfare Effects of Coordinated Assignment: Evidence from the NYC HS Match , 2015 .

[55]  M. Jackson,et al.  Envy-freeness and implementation in large economies , 2007 .

[56]  Bettina Klaus,et al.  Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems , 2003, Soc. Choice Welf..

[57]  M. Utku Ünver,et al.  Research Note - Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies , 2008, Mark. Sci..

[58]  D. J. Roberts,et al.  THE INCENTIVES FOR PRICE-TAKING BEHAVIOR IN LARGE EXCHANGE ECONOMIES , 1976 .

[59]  Parag A. Pathak,et al.  School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation. NBER Working Paper No. 16783. , 2011 .

[60]  Ali Hortaçsu,et al.  Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market , 2010, Journal of Political Economy.

[61]  Robert B. Wilson.  Game-Theoretic Analysis of Trading Processes. , 1985 .

[62]  Adam Szeidl,et al.  Contagion and State Dependent Mutations , 2003 .

[63]  Daniel R. Vincent,et al.  Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model , 2010 .

[64]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[65]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

[66]  Jakub Kastl.  Discrete Bids and Empirical Inference in Divisible Good Auctions , 2011 .

[67]  SangMok Lee,et al.  Incentive Compatibility of Large Centralized Matching Markets , 2017 .

[68]  Eduardo M. Azevedo,et al.  A Supply and Demand Framework for Two-Sided Matching Markets , 2014, Journal of Political Economy.

[69]  Ilya Segal,et al.  Optimal Pricing Mechanisms with Unknown Demand , 2002 .

[70]  L. Hurwicz.  On informationally decentralized systems , 1977 .

[71]  Paul Milgrom,et al.  Putting Auction Theory to Work , 2004 .

[72]  P. Hammond.  Straightforward Individual Incentive Compatibility in Large Economies , 1979 .

[73]  Loretta J. Mester,et al.  Uniform-Price Auctions : Update of the Treasury Experience , 1998 .

[74]  Jeffrey C. Ely,et al.  Foundations of Dominant Strategy Mechanisms , 2007 .

[75]  D. Bergemann,et al.  Robust Mechanism Design , 2003 .

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

[77]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[78]  Anna R. Karlin,et al.  On profit maximization in mechanism design , 2007 .

[79]  S. Pápai,et al.  Strategyproof and Nonbossy Multiple Assignments , 2001 .

[80]  Parag A. Pathak,et al.  School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation , 2011 .

[81]  Paulo Somaini,et al.  Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism , 2014 .

[82]  Yan Chen,et al.  School Choice : An Experimental Study ∗ , 2004 .

[83]  Yeon-Koo Che,et al.  Expanding 'Choice' in School Choice , 2008 .

[84]  Umut Mert Dur,et al.  The modified Boston mechanism , 2019, Math. Soc. Sci..

[85]  Parag A. Pathak,et al.  Appendix to "Incentives and Stability in Large Two-Sided Matching Markets" , 2009 .

[86]  Sven Seuken,et al.  Trade-offs in School Choice: Comparing Deferred Acceptance, the Naive and the Classic Boston Mechanism , 2014 .

[87]  M. Jackson,et al.  Approximately competitive equilibria in large finite economies , 1997 .

[88]  Parag A. Pathak,et al.  Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism , 2008 .

[89]  Benny Moldovanu,et al.  Bayesian and Dominant Strategy Implementation Revisited , 2011 .

[90]  Paul Milgrom,et al.  Critical Issues in the Practice of Market Design , 2011 .

[91]  Alex Rees-Jones,et al.  Suboptimal Behavior in Strategy-Proof Mechanisms: Evidence from the Residency Match , 2016, Games Econ. Behav..

[92]  Jeroen M. Swinkels.  Efficiency of Large Private Value Auctions , 2001 .

[93]  Paul Milgrom,et al.  Core-selecting package auctions , 2008, Int. J. Game Theory.

[94]  Aaron L. Bodoh-Creed.  Approximation of Large Games with Applications to Uniform Price Auctions , 2011, AMMA.

[95]  A. Roth.  The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics , 2002 .

[96]  Eric Budish,et al.  The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes , 2010, Journal of Political Economy.

[97]  R. Vohra,et al.  Market Research and Market Design , 2003 .

[98]  M. Pycia,et al.  Ordinal Efficiency, Fairness, and Incentives in Large Markets , 2016 .

[99]  M. Utku Ünver,et al.  Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies , 2007 .

[100]  R. Myerson.  Incentive Compatibility and the Bargaining Problem , 1979 .

[101]  Parag A. Pathak,et al.  Changing the Boston School Choice Mechanism , 2006 .

[102]  Narasimhan Jegadeesh,et al.  Treasury Auction Bids and the Salomon Squeeze , 1993 .

[103]  Antonio Miralles,et al.  School Choice: The Case for the Boston Mechanism , 2009, AMMA.

[104]  Yeon-Koo Che,et al.  Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms , 2008 .

[105]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

[106]  John William Hatfield,et al.  Strategy-proof, efficient, and nonbossy quota allocations , 2009, Soc. Choice Welf..

[107]  Arunava Sen,et al.  Ordinally Bayesian incentive compatible voting rules , 2004 .

[108]  Fuhito Kojima,et al.  Incentives in the probabilistic serial mechanism , 2010, J. Econ. Theory.

[109]  Navin Kartik,et al.  Strategic Communication with Lying Costs , 2009 .

[110]  Jerry R. Green,et al.  Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods , 1977 .

[111]  E. Maskin,et al.  Implementation Theory∗ , 2002 .

[112]  Scott Duke Kominers,et al.  Strategy-proofness, investment efficiency, and marginal returns: an equivalence , 2014, EC.

[113]  Sam Hwang,et al.  A Robust Redesign of High School Match , 2015, EAI Endorsed Trans. Serious Games.

[114]  Gabriel D. Carroll.  A Quantitative Approach to Incentives: Application to Voting Rules (Job Market Paper) , 2011 .

[115]  Alex Gershkov,et al.  On the equivalence of Bayesian and dominant strategy implementation for environments with nonlinear utilities , 2019 .

[116]  Jeroen M. Swinkels,et al.  EFFICIENCY OF LARGE DOUBLE AUCTIONS , 2003 .

[117]  S. Zamir,et al.  Formulation of Bayesian analysis for games with incomplete information , 1985 .

[118]  Judd B. Kessler,et al.  Course Match: A Large-Scale Implementation of Approximate Competitive Equilibrium from Equal Incomes for Combinatorial Allocation , 2015, Oper. Res..

[119]  Alvin E. Roth,et al.  The Economics of Matching: Stability and Incentives , 1982, Math. Oper. Res..

[120]  Robert J. Aumann,et al.  EXISTENCE OF COMPETITIVE EQUILIBRIA IN MARKETS WITH A CONTINUUM OF TRADERS , 2020, Classics in Game Theory.

[121]  Bengt Holmstrom,et al.  GROVES' SCHEME ON RESTRICTED DOMAINS , 1979 .