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Social Choice and Welfare

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24.03.2021 | Original Paper

On incentive compatible, individually rational public good provision mechanisms

verfasst von: Takashi Kunimoto, Cuiling Zhang

Erschienen in: Social Choice and Welfare | Ausgabe 2/2021

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Abstract

This paper characterizes mechanisms satisfying incentive compatibility and individual rationality in the classical public good provision problem. Many papers in the literature obtain the results in the so-called standard model of ex ante identical agents with a continuous, closed interval of types. The main contribution of this paper is the characterization of the budget-surplus maximizing mechanism satisfying incentive compatibility and individual rationality (Theorem 1 for Bayesian implementation and Theorem 3 for dominant strategy implementation) that applies to a finite discretization over the standard model. Making use of the proposed budget-surplus maximizing mechanisms, we show that some known results do not need the agents’ risk neutrality, whereas some others do rely on the agents’ risk neutrality in a subtle manner. Furthermore, we improve upon some known results and obtain new results which do not exist in the standard model.

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The reader is referred to Chapter 3.3 of Börgers (2015) for the textbook treatment of the classical public good problem with identical agents whose type space constitutes a continuous, closed interval on the real line.

The VCG mechanism is based on the contribution of Vickrey (1961), Clarke (1971), and Groves (1973). The reader is referred to Krishna and Perry (2000, Subsection 5.2) for the definition of the generalized VCG mechanism.

In their Theorem 2, Mailath and Postlewaite (1990) show that if we are to find a mechanism maximizing the public good provision probability among all mechanisms satisfying BIC, IIR, and strong BB, we lose nothing to focus on mechanisms in which the probability depends only on the average virtual valuation.

The reader is referred to Chapter 4.3 of Börgers (2015) for the textbook treatment of the public good problem using DSIC and EPIR. Once again, a big difference from our paper is that Börgers’ type space is assumed to be a closed interval in the real line.

In the special case where each agent i is risk-neutral, i.e., his valuation for the provision decision is \(v(q,\theta _i) = q \theta _i\) for each \(q \in [0,1]\) and \(\theta _i \in \Theta\), our nonnegative type assumption is consistent with the nonnegative valuation assumption which will be introduced later.

After introducing the formal definition of IIR, we will show that if the valuation functions are nonnegative valued, the IIR constraints can be incorporated into part of the BIC constraints by introducing a dummy type. Due to this methodology we employ, we exclude negative valuations.

Saijo and Yamato (1999) assume instead that each agent can not be excluded from the consumption of the public good even if he decides not to participate in the mechanism. Although the individual rationality of Saijo and Yamato (1999) is a lot more demanding than our IIR, we nevertheless establish a few negative results. Thus, we rather stick to our weaker individual rationality. The reader is referred to Saijo and Yamato (1999) for the discussion of their individual rationality constraints. Yenmez (2013) considers a similar constraint in a one-to-one matching environment.

Hellwig (2003) points out that this assumption is crucial for the result. Indeed, he completely overturns the result of Mailath and Postlewaite (1990) by isolating the effect of changes in the number of participants, while keeping cost technologies fixed.

Heydenreich et al. (2009), Carbajal and Müller (2015), and Edelman and Weymark (2020) all employ a graph theoretic approach to characterize dominant strategy incentive compatibility and revenue equivalence. Moreover, Heydenreich et al. (2009) state in their footnote 3 that with appropriate adjustments, their characterization of revenue equivalence extends to the case of Bayesian incentive compatibility, as we do here.

An arc \((\theta ^n, \theta ^m)\) can be transversed from \(\theta ^n\) to \(\theta ^m\) but not the other way around.

We impose the restriction \(n \ne m\) to avoid the self-loop which is an arc from a node to itself.

A cycle is a path whose initial and terminal nodes are the same.

Our Lemma 2 also follows from Observation 2 and Lemma 1 of Heydenreich et al. (2009), both of which are the allocation graph counterpart of Theorem 4.6.1 and Corollary 3.4.2 of Vohra (2011), respectively. Although Observation 2 is concerned with dominant strategy implementation, Heydenreich et al. (2009, footnote 3 and p.312) say that their analysis extends to Bayesian implementation and type graphs.

The existence of such a decision rule is automatically guaranteed because we consider the mechanism (x, t) such that the public good is never provided and no transfers are made. Such x is an IBN decision rule.

The tight mechanism was originally proposed by Kos and Manea (2009) in a bilateral trade environment. We adapt it to our public good environment.

The existence of such a sequence is automatically guaranteed because we consider the mechanism (x, t) such that the public good never be provided and no transfers be made. Such a mechanism trivially satisfies BIC, IIR, and BB and it works for any number of agents. Moreover, since the public good is never provided, the interim expected probability that the public good is provided is always zero for any agent of any type. Hence, Condition \(\alpha\) is trivially satisfied in this case.

Our Lemma 6 also follows from Observation 2 and Lemma 1 of Heydenreich et al. (2009), both of which are the allocation graph counterpart of Theorem 4.2.1 and Corollary 3.4.2 of Vohra (2011), respectively. See Heydenreich et al. (2009, p.312) where they say “One can check that all previous arguments still apply when using type graphs.”

The tight mechanism also generates ex post budget deficit at \((\theta ^M, \ldots , \theta ^M)\) even if we weaken strong BB into our BB constraint. This is because our BB is equivalent to strong BB at the type profile \((\theta ^M,\ldots ,\theta ^M)\), due to our richness condition.

Abreu D, Matsushima H (1992) Virtual implementation in iteratively undominated strategies: complete information. Econometrica 60:993–1008CrossRef

Börgers T (2015) An introduction to the theory of mechanism design. Oxford University Press, OxfordCrossRef

Carbajal JC, Müller R (2015) Implementability under monotonic transformations in differences. J Econ Theory 160:114–131CrossRef

Clarke E (1971) Multipart pricing of public goods. Public Choice 2:19–33

Dantzig GB (1998) Linear programming and extensions. Princeton University Press, Princeton

Edelman PH, Weymark JA (2020) Dominant strategy implementability and zero length cycles. Econ Theory. https://doi.org/10.1007/s00199-020-01324-7CrossRef

Green J, Laffont JJ (1977) Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica 45:427–438CrossRef

Groves T (1973) Incentives in teams. Econometrica 41:617–631CrossRef

Grüner HP, Koriyama Y (2012) Public goods, participation constraints, and democracy: a possibility theorem. Games Econ Behav 75:152–167CrossRef

Hellwig M (2003) Public-good provision with many participants. Rev Econ Stud 70:589–614CrossRef

Heydenreich B, Müller R, Uetz M, Vohra RV (2009) Characterization of revenue equivalence. Econometrica 77(1):307–316CrossRef

Kos N, Manea M (2009) Efficient trade mechanism with discrete values. Working paper

Krishna V (2009) Auction theory, 2nd edn. Academic Press, Cambridge

Krishna V, Perry M (2000) Efficient mechanism design. Mimeo, New York

Kuzmics C, Steg J-H (2017) On public good provision mechanisms with dominant strategies and balanced budget. J Econ Theory 170:56–69CrossRef

Lovejoy WS (2006) Optimal mechanisms with finite agent types. Manag Sci 52:788–803CrossRef

Mailath GJ, Postlewaite A (1990) Asymmetric information bargaining problems with many agents. Rev Econ Stud 57:351–367CrossRef

Mas-Colell A, Whinston M, Green J (1995) Microeconomic theory. Oxford University Press, Oxford

Saijo T, Yamato T (1999) A voluntary participation game with a non-excludable public good. J Econ Theory 84:227–242CrossRef

Schweizer U (2006) Universal possibility and impossibility results. Games Econ Behav 57:73–85CrossRef

Segal I, Whinston MD (2011) A simple status quo that ensures participation (with application to efficient bargaining). Theor Econ 6:109–125CrossRef

Serizawa S (1999) Strategy-proof and symmetric social choice functions for public good economies. Econometrica 67:121–145CrossRef

Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J Financ 16:8–37CrossRef

Vohra RV (2005) Advanced mathematical economics. Routledge, Oxfordshire

Vohra RV (2011) Mechanism design: a linear programming approach. Cambridge University Press, CambridgeCrossRef

Williams S (1999) A characterization of efficient, Bayesian incentive compatible mechanisms. Econ Theory 14:155–180CrossRef

Yenmez MB (2013) Incentive-compatible matching mechanisms: consistency with various stability notions. Am Econ J: Microecon 5:120–141

Titel: On incentive compatible, individually rational public good provision mechanisms
verfasst von: Takashi Kunimoto
Cuiling Zhang
Publikationsdatum: 24.03.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 2/2021
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-021-01329-8

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