Strategy-proofness in the Large

Abstract

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 strategyproofness (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: (i) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (ii) 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 strategy-proofness, which evaluates incentives to manipulate ex post, and the traditional notion of approximate Bayes-Nash incentive compatibility, which evaluates incentives to manipulate ex interim with respect to the single common-knowledge probability distribution associated with Bayes-Nash equilibrium. * First version: October 2011. We thank the editor and four anonymous referees for comments and suggestions that improved the paper considerably. We are grateful to

Double auction with interdependent values: Incentives and efficiency

“…More recently, Roth and Peranson (1999), Immorlica and Mahdian (2005), Kojima and Pathak (2009), Lee (2017), and Ashlagi et al (2017) show that the deferred acceptance algorithm due to Gale and Lloyd (1962) becomes increasingly hard to manipulate in large markets. In the object allocation setting without transfers, asymptotic incentive compatibility and asymptotic efficiency of various mechanisms have been established by Kojima and Manea (2010), Che and Kojima (2010), Liu and Pycia (2016), and Azevedo and Budish (2013). Our paper identifies another case in which both incentive compatibility and efficiency become achievable in large economies, reinforcing the insights from these existing studies.…”

“…In fact, as mentioned below, exact efficiency is not achievable. 4 Azevedo and Budish (2013) provide mechanisms that are approximately, but not exactly, incentive compatible. The main goal of the current study is different in that we obtain an exactly incentive compatible mechanism, but the basic motivation is similar.…”

A theory of school-choice lotteries

“…However, recent work suggests that these considerations are likely to be mitigated for large populations (cf. Manea 2010, Azevedo andBudish 2013). Indeed, we show that in a large market with diverse preference types of students, FDA becomes strategy-proof (Theorem 7).…”

“…However, in sufficiently large markets, nonstrategy-proof mechanisms of small markets can turn out to be strategy-proof (cf. Manea 2010, Azevedo andBudish 2013). Indeed, in a large market with diverse preference types of students, FDA is strategy-proof.…”

A Compact, Logical Approach to Large-Market Analysis

“…Infinite models are used frequently in game/economic theory as a way of representing limit-or "large"-markets. Some "large market" models feature continua of agents, with each agent having a negligible contribution to the overall market (see, e.g., Aumann and Shapley, 1974;Gretsky et al, 1992Gretsky et al, , 1999Kaneko and Wooders, 1986;Azevedo et al, 2013;Nöldeke and Samuelson, 2018;Azevedo and Budish, 2019;Greinecker and Kah, 2019). A second class of models has worked with either discrete infinite markets (Fleiner, 2003;Kircher, 2009;Jagadeesan, 2018a) or a limit of finite markets (Immorlica and Mahdian, 2005;Kojima and Pathak, 2009;Ashlagi et al, 2014).…”