Transient nature of cooperation by pay-it-forward reciprocity

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.


Supplementary Information
for "Transient nature of cooperation by pay-it-forward reciprocity" by Horita, Takezawa, Kinjo, Nakawake, and Masuda Figure S1: Exemplar decision screens Figure S2: Relationship between R (= p(C|C) − p(C|D)) in the two types of game Figure S3: Schematic of chains of decisions consisting of five participants Figure S4: Schematic of two simultaneously running chains Figure S5: Schematic of the two-state Markov chain model

Supplementary Figures
Supplementary Tables  Table S1: Statistics of the groups of participants Table S2: Selection of the multivariate GLMM containing up to three-way interaction Table S3: Analysis of the best GLMM containing up to three-way interaction Table S4: Population averages of p(C|C) and p(C|D) in each round and type of game Table S5: Univariate GLMM analysis Table S6: Multivariate GLMM analysis when both the individual and the group were added as random effects Table S7: Multivariate GLMM analysis in the pay-it-forward game with an additional interaction term, i.e., interaction between the decision of the previous participant and the SVO

Supplementary Methods
Running chains of decisions Questionnaire used for measuring social value orientation Maximum likelihood estimate for the two-state Markov chain

Supplementary Figures
Supplementary Figure S1: Exemplar decision screens. (a) Pay-it-forward game, (b) Reputation-based game. The captions displayed to the participants were written in Japanese.
Here we translated them into English.  Figure S4: Schematic of two simultaneously running chains. The case of the pay-it-forward game is shown for expository purposes.

Supplementary Tables
Supplementary Table S1: Statistics of the groups of participants. In group 4, one participant did not report his/her gender when registering to the participant pool. In the row "order of games", P-R indicates that the participants first played the pay-it-forward game and then the reputation-based game. R-P indicates the opposite order of the games. Order of games P-R R-P P-R R-P P-R R-P P-R Supplementary We carried out GLMM analysis including up to the three-way interaction term, "DPP x round x game type", where DPP stands for the decision of the previous participant. The independent variables were the decision of the previous participant (D = 0, C = 1), SVO (pro-self = 0, pro-social = 1), round (integer valued, ranging from 1 to 45), gender (female = 0, male = 1), and game type (reputation-based game = 0, pay-it-forward game = 1). The dependent variable was the participant's decision (D = 0, C = 1). We examined 16 models in which each of the four possible two-or threeway interaction terms were switched on or off. The four possible interaction terms were "DPP x round", "DPP x game type", "round x game type", and "DPP x round x game type". In the table, the interaction terms added and not added to the GLMM are represented by 1 and 0, respectively. For each estimated GLMM, we calculated the Akaike's information criterion (AIC). We found that model 9, which did not include "DPP x round" and did include the other two two-way interaction terms and the sole three-way interaction term, realized the smallest AIC value.

Running chains of decisions
In each type of game, the participants were embedded in chains and made decisions about 40 times. A schematic of a group of five participants engaged in the pay-it-forward reciprocity game is shown in Supplementary Fig. S3(a). Player V, W, X, Y, and Z made decisions in this order. It should be noted that, to make a decision, W referred to the decision that V had made toward W. Similarly for X, Y, and Z. When Z's decision finished, the positions of the five participants were shuffled such that the upstream and downstream neighbors of each participant were those who the participant had not interacted in the first decision. For example, W's neighbors were V and X in the first decision and Y and Z in the second decision. This treatment excludes possibilities of direct reciprocity, which would occur when the same players meet repeatedly. We assumed that the first player was always the same right after shuffling (i.e., V in Fig. S3(a)). However, this assumption was immaterial. Then, the five participants sequentially made their second decisions. Then, the positions of the participants were reshuffled such that each participant avoided anybody that the participant had as a neighbor previously. We continued the decisions and shuffling until we exhausted all possible participants as neighbors. Because each decision consumed two other participants as neighbors of a given participant, there were T decision opportunities for a group of 2T+1 participants in one chain.
Participants were assigned computer-generated random three-letter names, which were displayed on their screens (see Supplementary Fig. S1). Prior to each decision, the participants received new and unique three-letter names. In Supplementary Fig. S3(a), player W received name "hky" in the first decision and "ziw" in the second decision. This treatment intended to make participants feel that they were interacting with strangers in every decision.
Supplementary Fig. S3(b) schematically depicts a chain of decisions with five participants engaged in the reputation-based game. First, V made a decision toward X. It should be noted that V did not refer to X's previous decision, which did not exist at this stage. Therefore, we excluded V's first decision from the analysis. Second, Z made a decision toward V, referring to the decision that V had made toward X. Similarly for W, Y, and X. When X's decision finished, the positions of the five participants were randomly shuffled in the same way as in the pay-it-forward game. Then, the participants sequentially made the second decision. We continued the decisions and shuffling until we exhausted all possible participants as neighbors.
As in the pay-it-forward game, the participants received computer-generated unique threeletter names prior to each decision.
One group consisted of 17 or 19 participants. Therefore, if a single chain were run as we explained with Supplementary Fig. S3, a participant would have to wait for 16 or 18 participants' decisions until the next decision opportunity on average. The mean response time was equal to 3.99 sec, which would lead to the mean waiting time of 3.99 x 16 = 63.84 sec. Then, the participants would easily get bored. Therefore, we simultaneously ran multiple chains of decisions. If the decision opportunity arrived at a participant too frequently, the participant would have doubted that he/she was embedded in the chain as a natural interpretation of the instructions would stand.
Therefore, we simultaneously ran five chains as follows. Here, we explain a simplified case of two chains and a group of five players ( Supplementary Fig. S4). Initially, the five participants were randomly ordered in each of the two chains. In this example, "asu" and "akh" first made decisions in chains 1 and 2, respectively. When both "asu" and "akh" submitted the decisions, the decision screens were simultaneously displayed to the next player in each chain, i.e.,"hky" and "zyx". We repeated this procedure. We assured that the same player did not appear in different chains at the same time. When the fifth participant submitted the decision in both chains, two rounds were completed. It should be noted that the round was defined as the number of decisions that a participant made regardless of the chain in which the participant responded. In Supplementary Fig. S4, two participants simultaneously making decisions in the different chains may be in different rounds. For example, X and W under the anonymous names "bwx" and "stt" in Supplementary Fig. S4 are in their first and second rounds, respectively.
As mentioned above, a player never saw the same neighbor within each chain. However, they may have played with same participants in different chains. This fact was not problematic because each participant received different three-letter names in different chains and rounds.
Prior to the experiment, participants were informed of the structure of the simultaneously running chains of decisions.
In a group of 19 participants, a participant made decisions nine times in a chain. When no failure occurred, the length of a chain was equal to 171 (= 19 participants x 9 decisions), and each participant submitted 45 decisions (= 9 decisions x 5 chains) in each type of game.
Questionnaire used for measuring social value orientation Question 1: A: You get 480 yen, and the partner gets 80 yen. B: You get 540 yen, and the partner gets 280 yen. C: You get 480 yen, and the partner gets 480 yen.
Question 2. A: You get 560 yen, and the partner gets 300 yen. B: You get 500 yen, and the partner gets 500 yen. C: You get 500 yen, and the partner gets 100 yen.
Question 3. A: You get 520 yen, and the partner gets 520 yen. B: You get 520 yen, and the partner gets 120 yen. C: You get 580 yen, and the partner gets 320 yen.
Question 4. A: You get 500 yen, and the partner gets 100 yen. B: You get 560 yen, and the partner gets 300 yen. C: You get 490 yen, and the partner gets 490 yen.
Question 5. A: You get 560 yen, and the partner gets 300 yen. B: You get 500 yen, and the partner gets 500 yen. C: You get 490 yen, and the partner gets 90 yen.
Question 6. A: You get 500 yen, and the partner gets 500 yen.
B: You get 500 yen, and the partner gets 100 yen. C: You get 570 yen, and the partner gets 300 yen.
Question 7. A: You get 510 yen, and the partner gets 510 yen. B: You get 560 yen, and the partner gets 300 yen. C: You get 510 yen, and the partner gets 110 yen.
Question 8. A: You get 550 yen, and the partner gets 300 yen. B: You get 500 yen, and the partner gets 100 yen. C: You get 500 yen, and the partner gets 500 yen.
Question 9. A: You get 480 yen, and the partner gets 100 yen. B: You get 490 yen, and the partner gets 490 yen. C: You get 540 yen, and the partner gets 300 yen.
Maximum likelihood estimate for the two-state Markov chain The structure of the two-state Markov chain model is shown in Supplementary Fig. S5. The likelihood, denoted by L, with which a quadruple (n CC , n CD , n DC , n DD ), where n CC is the number of C after receiving/observing C, n CD is the number of D after receiving/observing C, n DC is the number of C after receiving/observing D, and n DD is the number of D after receiving/observing D, is given by L = p(C | C) n CC [1− p(C | C)] n CD p(C | D) n DC [1− p(C | D)] n DD . (S1) The maximum likelihood implies that ∂log L ∂p(C | C) = 0, which yields p(C | C) = n CC n CC + n CD .
Similarly, ∂log L ∂p(C | D) = 0 yields p(C | D) = n DC n DC + n DD . We used the estimated p(C|C) and p(D|D) (= 1 -p(C|D)) as p in equation (2) to derive the theoretical distributions of the length of C and that of D, respectively.