Transient nature of cooperation by pay-it-forward reciprocity

Abstract

Humans often forward kindness received from others to strangers, a phenomenon called the upstream or pay-it-forward indirect reciprocity. Some field observations and laboratory experiments found evidence of pay-it-forward reciprocity in which chains of cooperative acts persist in social dilemma situations. Theoretically, however, cooperation based on pay-it-forward reciprocity is not sustainable. We carried out laboratory experiments of a pay-it-forward indirect reciprocity game (i.e., chained gift-giving game) on a large scale in terms of group size and time. We found that cooperation consistent with pay-it-forward reciprocity occurred only in a first few decisions per participant and that cooperation originated from inherent pro-sociality of individuals. In contrast, the same groups of participants showed persisting chains of cooperation in a different indirect reciprocity game in which participants earned reputation by cooperating. Our experimental results suggest that pay-it-forward reciprocity is transient and disappears when a person makes decisions repeatedly, whereas the reputation-based reciprocity is stable in the same situation.

Figure 1. Schematic of the indirect reciprocity games.

(a) Pay-it-forward game. (b) Reputation-based game. Each participant received random three-letter names.

Figure 2. Time courses of the fraction of cooperation averaged over all participants.

A round corresponds to one decision made by each participant (e.g., the third round implies the third decision made by each participant in the entire game). (a) p(C) in the pay-it-forward game, (b) p(C) in the reputation-based game, (c) p(C|C) in the pay-it-forward game, (d) p(C|C) in the reputation-based game, (e) p(C|D) in the pay-it-forward game, and (f) p(C|D) in the reputation-based game. The error bars represent 95 % confidence intervals (±1.96 × SE).

Figure 3. The relationship between the probability of cooperation in the pay-it-forward game and that in the reputation-based game.

A circle represents a participant. The solid lines represent the linear regression. (a) p(C), (b) p(C|C), and (c) p(C|D).

Figure 4. Frequencies of the length of cooperation and that of defection.

The bars represent empirical frequencies. There were some samples that had run lengths larger than ten and hence were not shown in each panel. The solid and dashed curves represent the geometric distributions estimated based on the i.i.d. and Markov assumptions, respectively. (a,b) show the frequencies of the length of C in the pay-it-forward game and those in the reputation-based game, respectively. In (a), both solid and dashed lines are based on p ≈ 0.42. In (b), the solid line is based on p = 0.60, and the dashed line is based on p = 0.71. (c,d) show the frequencies of the length of D in the pay-it-forward game and those in the reputation-based game, respectively. In (c), both solid and dashed lines are based on p ≈ 0.58. In (d), the solid line is based on p = 0.40, and the dashed line is based on p = 0.53. The solid and dashed lines almost completely overlap in (a,c).