An experimental comparison of collective choice procedures for excludable public goodsIntroductionThe modelProperties of SCS, PCS and NRSerial cost sharingProportional cost sharing (PCS)Cost sharing with NRExperimental parametersEquilibria in SCSEquilibria in PCS and NREx post efficiency of equilibria in SCS, PCS and NREx ante efficiency of equilibria in SCS, PCS and NRHypothesesExperimental designResultsIndividuals: bidding behaviorBidding behavior in SCS: a quantal response explanation for disequilibrium bidsComparing bids under PCS and NRBidding behavior in NR and PCS and equilibrium predictionsOther explanations for deviations from equilibrium behaviorRisk aversion as a possible explanation of overbiddingLearningGroups: efficiency comparisonsSurplus extractionProportion of efficient decisionsRobustness of efficiency results to other environmentsConclusionsAcknowledgementsInstructionsDecision making experimentSerial cost sharingProportional cost sharingNo rebatesProofs of Propositions 6-8ReferencesAn experimental comparison of collective choiceprocedures for excludable public goodsSean Gailmarda, Thomas R. Palfreyb,*aDepartment of Political Science, Northwestern University, United StatesbDepartment of Politics and Economics, Princeton University, United StatesReceived 13 March 2002; received in revised form 28 December 2002; accepted 23 April 2003Available online 14 November 2004AbstractThis paper compares three collective choice procedures for the provision of excludable publicgoods under incomplete information. One, serial cost sharing (SCS), is budget balanced, individuallyrational, anonymous and strategy proof. The other two are bhybridQ procedures: voluntary costsharing with proportional rebates (PCS) and with no rebates (NR). PCS satisfies all these propertiesexcept strategy proofness, and NR satisfies all the properties except for strategy proofness andbudget balance. However, PCS and NR do not exclude any potential users, and they do not requireequal cost shares, thereby overcoming the two main sources of inefficiency with SCS. Wecharacterize the Bayesian Nash equilibria (BNE) of the hybrid mechanisms and conduct laboratoryexperiments to compare the performance of the three mechanisms. We find that PCS producessignificantly more efficient allocations than either SCS or NR.D 2004 Elsevier B.V. All rights reserved.Keywords: Serial cost sharing; Proportional rebates; No rebates1. IntroductionFor the last several decades, economists and Social Scientists have grappled with thequestion of how to design mechanisms for the efficient production and cost sharing ofpublic goods. Nearly all of the energy has been directed toward the case of pure,0047-2727/$ - see front matter D 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.jpubeco.2003.04.002* Corresponding author. Tel.: +1 609 258 4031; fax: +1 609 258 8854.E-mail addresses: [email protected] (S. Gailmard)8 [email protected] (T.R. Palfrey).Journal of Public Economics 89 (2005) 1361 – 1398www.elsevier.com/locate/econbasenonexcludable public goods. While the reasons for focusing on that kind of public goodare historical and well rooted in the traditional literature, it is not at all clear that this is themost typical case in practice. Many public goods are excludable. Even the classicexamples like lighthouses, parks and security can, in principle (and often do, in practice),exclude some users.Recently, there has been an upsurge of interest in the design of mechanisms forexcludable public goods.1These mechanisms focus largely on cost sharing schemes,which assign different levels of usage to different consumers, and have a formula forassigning cost shares based on level of usage. The threat to exclude can serve to relaxincentive constraints. But this comes with a cost, and this cost has been largely ignoredin the literature. The very act of exclus ion creates inefficiencies in a very direct way,which we call exclusionary inefficiency. Once a public good is provided, it is costless toallow extra users, so it is inefficient to exclude.2A subset of the mechanisms forproduction and cost sharing of excludable public goods are mechanisms that excludenobody. In mechanisms of this sort , there is no exclusionary inefficiency, so the onlysource of inefficiency is from free riding problems that result in underproduction of thepublic good.In this paper, we report on experiments for the provision of excludable threshold publicgoods, and compare the performance of a widely acclaimed cost sharing mechanism, serialcost sharing, with two very simple and practical nonexclusionary rules, which are variantsof a voluntary contributions mechanism. To keep the experiment as simple as possible, andto be able to compute Bayesian Nash equilibria (BNE) of the voluntary contributionsmechanisms, we consider a discrete public good technology where, if a certain thresholdof contributions is met, the good is produce d and may be consumed at no extra cost to anysubset of the group; the good is not produced at all if the threshold is not met. Consumershave private valuations of the public good and there is incom plete information about thesepreferences.The basic question at issue here is whether the excellent incentive properties of theserial cost sharing (SCS) mechanism also imply good efficiency properties, relative tomechanisms that require ex post individual rationality. Since we are in a second bestworld, it does not make sense to compare serial cost sharing to the first bestallocation, a comparison in which it would fare poorly. Instead, a natural benchmarkis to compare serial cost sharing to mechanisms that are practical to implement andare widely observed. For this reason, we chose two variants on the voluntarycontributions mechanism. In these mechanisms, individuals simply make pledgestoward the production of the public good and the total production is simply theefficient production given the total amount of pledges.3In our discrete environment,this means that the public good is produced if and only if the sum of the pledgesexceeds the threshold, or cost of product ion. Mechanisms of this sort resemble fund1See, for example, Moulin (1994), Deb and Razzolini (1999), Chen and Khoroshilov (2003), Chen (2003),Dorsey et al. (2002) and Norman (2000).2This is true for nonrival public goods. In case of crowding or other sorts of user externalities, the inefficienciescreated by exclusion are less severe and exclusion can even be efficiency