Partners versus Strangers: Random Rematching in Public Goods ExperimentsIntroductionPartners versus StrangersA Closer LookPartners, Strangers, Warm-glow and ConfusionWhat is Next?ReferencesProvided for non-commercial research and educational use only.Not for reproduction, distribution or commercial use.This chapter was originally published in the book Handbook of ExperimentalEconomics Results. The copy attached is provided by Elsevier for the author’s benefitand for the benefit of the author’s institution, for noncommercial research, andeducational use. This includes without limitation use in instruction at your institution,distribution to specific colleagues, and providing a copy to your institution’sadministrator.All other uses, reproduction and distribution, including without limitation commercialreprints, selling or licensing copies or access, or posting on open internet sites, yourpersonal or institution’s website or repository, are prohibited. For exceptions,permission may be sought for such use through Elsevier’s permissions site at:http://www.elsevier.com/locate/permissionusematerialJames Andreoni and Rachel Croson, Partners versus Strangers: Random Rematchingin Public Goods Experiments. In: C.R. Plott and V.L. Smitt, editors, Handbook ofExperimental Economics Results, Volume 1. Amsterdam: North-Holland, 2008,p. 776.ISBN: 978-0-444-82642-8© Copyright 2008 Elsevier B.V.Author’s personal copyChapter 82PARTNERS VERSUS STRANGERS:RANDOM REMATCHING IN PUBLIC GOODS EXPERIMENTSJAMES ANDREONIDepartment of Economics, University of Wisconsin–Madison, Madison, Wisconsin 53711, USARACHEL CROSONUniversity of Texas at Dallas, 2601 N. Floyd Road, P.O. Box 830688, GR 31,Richardson, TX 75083-0688, USAe-mail: [email protected]. IntroductionHow can an experimenter balance the desire to test a single-shot Nash equilibrium pre-diction with the need for repeated experience by subjects? Simply repeating the gamewith the same set of subjects may change the nature of equilibrium, since incompleteinformation about “types” can lead to reputation effects of the sort described by Krepset al. (1982). A common way to deal with this has been to rematch subjects randomlyinto groups for each iteration of the game, hence forming a repeated single-shot designand avoiding the repeated-game effects. This raises the natural question: what is theeffect of random rematching?The rematching of subjects in linear public goods experiments was introduced byAndreoni (1988). The first linear public goods experiments, by Marwell and Ames(1981), were single-shot games and produced little of the dominant strategy Nash equi-librium free riding they predicted. Subjects, it was argued, needed experience to learnthe dominant strategy. Isaac and Walker (1988) replicated these games, but used a 10-period, finitely repeated game. However, free riding was still not chosen, and repetitionhad only a small effect in increasing free riding. Was it reputation effects that kept sub-jects from adopting the single-shot dominant strategy?Andreoni (1988) tested this question by comparing a set of subjects who played infinitely repeated games with another set who played in a repeated single-shot. Players inthe repeated game were called “Partners,” while those in the repeated single-shot gamewere called “Strangers.” If reputations matter, then Partners should cooperate more thanStrangers. Surprisingly, Andreoni found just the opposite – Strangers cooperated signif-icantly more than Partners.Since this time, many researchers have explored this anomalous result. This chapterwill attempt to synthesize the various replications and studies that have addressed thispuzzle.Handbook of Experimental Economics Results, Volume 1Copyright © 2008 Elsevier B.V. All rights reservedDOI: 10.1016/S1574-0722(07)00082-0Author’s personal copyCh. 82: Partners versus Strangers: Random Rematching in Public Goods Experiments 7772. Partners versus StrangersLinear public goods experiments can be described simply. Individuals are given a budgetm of tokens which they can “invest” in a public good, g, or a private good, x, hencex + g = m. Payoffs to any subject i are determined by Pi= xi+ αnjgj, where n isthe number of group members. The parameter α is chosen such that 0 <α<1, hencefree riding, g = 0, is a single-shot dominant strategy, and such that nα > 1, so thatg = m for all i is the symmetric Pareto efficient outcome.Andreoni examined groups of five players, with α = 0.5, in ten-period games. In eachsession of the Strangers treatment, 20 subjects were randomly rematched into groupsof five after each play of the game, while a comparable set of Partners played in anadjacent room.1Andreoni also included another design twist intended to test learningeffects. After ten periods subjects were told they would “restart” the experiment foranother ten rounds – if no learning effects are present, the restart should have no effect.Due to budget constraints, the restart ended after three periods. Andreoni’s results areplotted in Figure 1A.The nearest replication to Andreoni’s experiment was performed by Croson (1996).Again using α = 0.5, ten periods, and a surprise ten-period restart, Croson consideredfour person groups.2A plot of the data by Croson is shown in Figure 1B.We can see that Andreoni and Croson get different results for the first ten periods– Croson finds Partners are significantly more cooperative, while Andreoni finds it isStrangers. Looking at the restart, however, both find similar results. For Partners theeffect of the restart is far more pronounced, indicating that for both experiments thereis some effect of repeated play. Given the contradictory effects of the first ten periods,however, one must ask whether the effect of repeated play is on reputations or somethingelse.Several other authors have also compared Partners to Strangers in experiments.A summary of these results is given in Table 1. All of these experiments differ in sundryways from either Andreoni or Croson’s studies, so the comparisons to these results arenot precise. Nonetheless, this summary of results does little to clear up the picture. Inall, four studies find more cooperation among Strangers, five find more by Partners, andfour fail to find any difference at all.3. A Closer LookThe discussion of Partners versus Strangers thus far has been predicated on the assump-tion that the incentives of individuals are consistent with