Giving Little b y Little:Dynam ic Volun tary Con tribution G amesJohn Duffy, Jac k Oc hs and Lise Vesterlund∗Departm ent of EconomicsUniversit y of PittsburghPittsburgh, PA 15260This Draft:June 2005AbstractCharitable con tributions are frequently made over time. Donors arefree to contribute whenever they wish and as often as they want, andare frequently updated on the level of contributions by others. This dy-namic structure enables donors to condition their contribution on thatof others, and, as Schelling (1960) suggested, may serve to o vercomefree-riding thereby increasing charitable giving. Marx and Matthews(2000) build on Schelling’s insight and show that multiple contributionrounds may secure a provision level that cannot be achieved in the sta-tic, one-shot setting, but only if there is discrete, positive payoff jumpupon completion of the project. We examine these t wo hypothesesexperimentally using static and dynamic public good games. We findthat contributions are indeed higher in the dynamic than in the staticgame. However, in contrast to the predictions, the increase in contribu-tions in the dynamic game does not appear to depend on the existenceof a completion benefit jump or on whether players can condition theirdecisions on the beha vior of other members of their group.Keywords: Dynamic Public Goods Game, Voluntary Contribution Mech-anism, Information, Reciprocity.∗We acknowledge support from the National Science Foundation. We thank ScottKinross for invaluable research assistance.11IntroductionTheoretical analysis of voluntary contribution games suggests that free-riderproblems will hinder the financing of public goods. Nevertheless, some publicgoods are, in fact, financed through voluntary contributions. This observa-tion has led to a voluminous experimental literature aimed at understandingthe factors that influence the level of con tributions observed in voluntarycontribution games.Surprisingly, much of the theoretical and experimen tal work on voluntarycontributions has focused on static, as opposed to dynamic game environ-ments. In a static game, each player makes a single contribution decisionand that decision must be made without knowledge of the decisions made byothers. By contrast, in a dynamic game, players make decisions in multiplerounds and may condition each decision upon the level of total contributionsin the previous round, a state-variable that is periodically updated.There is good reason to think that charitable giving should be viewedas a dynamic rather than a static game. Certainly, most charities do notrequire that contributions be made at a single date in time — rather, mostfund-drives last for some duration of time, and a target goal is set in advance.Further, charities find it useful to periodically update potential donors onthe level of contributions received during the fund-drive. For instance, theUnited Way is fond of using “thermometers” showing progress made duringa campaign toward the target goal.Why might contribution decisions differ in a dynamic setting as opposedto a static one? Or equivalently why might behavior be sensitive to therebeing multiple rather than just one contribution round? Schelling (1960)suggested one possibility: dynamic environments allow for smaller, history-contingent contributions that reduce the cost of free—riding. Specifically,Schelling writes (1960, pp. 45-6):“Even if the future will bring no recurrence, it may be possible tocreate the equivalence of continuity by dividing the bargainingissue into consecutive parts. If each party agrees to send a mil-lion dollars to the Red Cross on condition the other does, eachmay be tempted to cheat if the other contributes first, and eachone’s anticipation of the other’s cheating will inhibit agreement.But if the contribution is divided into consecutive small contri-butions, each can try the other’s good faith for a small price.Furthermore, since each can k eep the other on short tether tothe finish, no one ever need risk more than one small contribu-1tion at a time. Finally, this change in the incentive structureitself takes most of the risk out of the initial contribution; thevalue of established trust is made ob viously visible...”Marx and Matthews (2000) build on Schelling’s insight regarding theimportance of history dependent contribu tions, and develop a theory of howagents might complete funding of a public good in a finite horizon game.Specifically, they show that if agents are payoff maximizers, the equilibria ofthe m ultiple contribution-round (dynamic) finite game will differ from theone-round (static) game only if a discrete benefit ‘jump’ is realized uponcompletion of the public good project. In particular, in the presence of abenefit jump, dynamic play may sustain equilibria that complete the publicgood (via history-dependent trigger strategies), even when no such equilibriaexist in the static, one-round contribution game with the same payoffs. Adiscrete completion benefit arises when the full benefits of a project are notexperienc ed until the project is completed. For example, contributions to thehomelessmayhavesomeimmediatebeneficial effect, but a substantial anddiscrete increase in benefits from contributions may not be achieved untilsufficient funds have been collected to build a homeless shelter. Similarly, acompleted collection of paintings may result in a larger overall benefitthanthesumofthebenefits associated with each individual painting. Publicradio fund-raising campaigns that promise to end early if their target isreached before the drive is up provide an endogenous and discrete completionbenefit.In this paper we report on a laboratory experiment designed to investi-gate these two theories. Specifically, we ask whether voluntary contributiondecisions differ when the con tribution game is dynamic rather than static,and if so, whether the differences are owing to the mechanisms suggestedby Schelling and Marx and Matthews. Consistent with their hypotheses, wecompare behavior when individuals with a given endowment simultaneouslycontribute in either one or multiple contribution rounds.1In the presenceof a completion benefit, differentia l behavior in the dynamic versus staticgames would be consistent with both Schelling and Marx and Matthews. To1Thus our study differs from the experimental literature on voluntary contribution smade by “partners” vs. “strangers,” where individuals p lay repeated