Vanishing Leadership and Declining Reciprocity in a Sequential Contribution Experiment

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I. INTRODUCTION

Contributing sequentially is a widespread practice for a large variety of public goods, ranging from dish washing in households to the ratification of international treaties by states. Academic research, free Wikipedia, and telethons are other popular examples. Contributions are not necessarily in monetary terms, but they share two important features: the amount of public good provided depends on some aggregation of individual contributions, and later contributors in a sequence can condition their contribution on previously observed contributions.

Surprisingly, the economic literature on sequential contributions is rather scarce, while an overwhelming bulk of knowledge has been accumulated on simultaneous contributions environments. Other things being equal, should one expect a higher level of public good provision when contributions are sequential? Getting back to the telethon example, does the publicly released information about contributions affect donations during the campaign?

The recent experimental literature about leading-by-example, based on the linear public good games, provides mixed evidence about the effect of sequentiality on the level of group contributions. The relevant papers are based on a procedure where the contribution of a first mover (leader) is publicly announced, and later movers contribute simultaneously. While this form of sequential moves tends to increase group contributions compared to simultaneous moves contribution games, the effect is not always significant. Taking the simultaneous contribution game as a benchmark, Guth et al. (2007) found a strong positive effect of this type of leadership, while Moxnes and van der Heijden (2003) found only a negligible (but significant) effect. Others found no significant difference in group contributions between sequential and simultaneous moves games (Potters, Sefton, and Vesterlund 2007; Rivas and Sutter 2009). (1,2) It is therefore fair to say that the available experimental evidence is mixed, and that more data are needed to understand and disentangle the various effects that contributing sequentially might induce. Some of these effects are already clearly established: there is robust evidence that first movers tend to make larger contributions than later movers, and that later movers' contributions are strongly correlated to the first mover's contributions, suggesting that sequentiality stimulates reciprocal behavior (Arbak and Villeval 2007; Gachter et al. 2009b; Guth et al. 2007; Levati, Sutter, and van der Heijden 2007; Pogrebna et al. 2009; Potters, Sefton, and Vesterlund 2007; Rivas and Sutter 2008). Similar observations were made in the sequential prisoners' dilemma game by Clark and Sefton (2001) who report that second movers tend to "cooperate" if the first mover chose to cooperate, and in field experiments (Martin and Randal 2005; Shang and Croson 2005).

Why do first movers contribute more than second movers and why--on average--are group contributions larger when individual contributions are ordered sequentially? Take the point of view of the first mover: he can have an incentive to make a large contribution either because he is aware that second movers observe his contribution decision (leading-by-example), or simply because he is assigned to the first mover's role (pure ordering effect). The experimental literature on common pool resource games documented significant order effects even if later decision makers cannot observe previous moves (see Budescu, Suleiman, and Rapoport 1995; Rapoport 1997; Rapoport, Budescu, and Suleiman 1993; Suleiman, Rapoport, and Budescu 1996). Whether or not such pure order effects also arise in voluntary contribution games remains an open question (however, see Guth, Huck, and Rapoport 1998).

Consider now the point of view of second movers: they may contribute less than first movers, either because of imperfect reciprocity, or because of an "end-of-sequence" effect. …