Resilient cooperators stabilize long-run cooperation in the finitely repeated Prisoner's Dilemma

Learning in finitely repeated games of cooperation remains poorly understood in part because their dynamics play out over a timescale exceeding that of traditional lab experiments. Here, we report results of a virtual lab experiment in which 94 subjects play up to 400 ten-round games of Prisoner's Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round of first defection moves earlier for several days; however, this unravelling process stabilizes after roughly one week. Analysing individual strategies, we find that approximately 40% of players behave as resilient cooperators who avoid unravelling even at significant cost to themselves. Finally, using a standard learning model we predict that a sufficiently large minority of resilient cooperators can permanently stabilize unravelling among a majority of rational players. These results shed hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of long-run experiments.


Fraction of strategies unclassified
Supplementary Figure 6 -Fraction of strategies classified as "other" (i.e. not CC or Threshold) by day. As discussed in the main text, we classified all players in terms of both their observed behavior from the data and also their self-declared strategies. On day 1 almost 20% of strategies cannot be classified, as players switch back and forth between cooperate and defect during an initial learning period. However, we note that even this fraction falls to roughly 2% by day 5 and remains close to zero for the rest of the experiment.  In the case of overall cooperation and day 1) we conducted pairwise t-tests, whereas for round 1 of game 1 we used pairwise Fisher's exact tests (because when comparing play in a single round we have only one observation per person). In all cases the tests were insignificant at 5%, hence we conclude that behavior in our experiment does not vary significantly with self-reported experience. Recall that β → 0 implies that each agent deterministically selects the strategy with the highest expected utility, whereas β → ∞ corresponds to agents making uniformly random choices of strategy (see Methods). Varying β by two orders of magnitude results in very similar predictions; thus we conclude that our simulation is not sensitive to this parameter over a wide range of values.Each line is the average of all rational agents in 10 sets of simulations with 100 agents each.

Comparison of Dropouts to Main Population
Supplementary Figure 11 -Daily cooperation rates of the 19 dropout players relative to the completed population over the same time period, shown as a standardized z-score. Shaded areas indicate the 5% most extreme values. Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 1 CC CC "I always chose 1, hoping to gain the others trust and get the most points." "I stopped pressing 2 when the other play pressed 2, and continued to press 1, hoping to gain their trust." 2 threshold threshold "I chose to cooperate for the first 8 rounds, and defect for the last 2, unless the other person defected before I did. . ." "Sometimes I chose to defect on the 7th or 8th round, as others seemed to start defecting in round 9." 3 CC CC "I chose to cooperate each round but did play defensively and defected if my partner did so before the last round." ". "If I felt that every person I was being partnered with was looking out for their own personal gain, then I would try to do the same. This only happened a few days for me." 6 threshold threshold "I settled on choosing 1 for the first 8 rounds and then selecting 2 for the remaining two rounds." "My initial strategy was selecting all choice 1 for every game/round no matter what. My strategy changed because of non-cooperative partners. . . My strategies overall went from all choice 1 to then selecting choice 2 for the last couple of rounds. I almost started doing choice 2 at round 8 as well but didn't do that much at all, I didn't like it." 7 threshold threshold "I started off by trying to cooperate to the positive each time. . . it seemed that many people were willing to go along and do all 10 rounds positively. . . but as time wore on, it became evident that I was only being cheated over and over again in the final rounds. . . I started to see my daily bonus go down, and inevitably began defecting first on the last round, then in the 9th, and finally in the 8th round to counteract/preempt the defect that almost always was inevitably coming." "Absolutely. For the first, maybe 10 games, I tried to go to the end, only defecting after someone else defected. . . I began to also defect in stages, (ie. first the 10th round, then into the 9th, and finally into the 8th). . ."

CC CC
"I wanted to my partner and I to cooperate so we could both make good money." "I was going to click all option 1's, but then the partner would choose option 2 about game 9 or 10, so I started doing the same some days, and some days I would pick option 1 every game no matter what just to see how much money I made." 9 threshold N/A "At the beginning I wanted to be fair and give each of me and the opposite player a fair chance at the money. . .Then I got "jaded" but the slower game players. . . if I suspected they were going to be one of the "problem" people, I would just start pressing the red one and not care about the money earned for myself. . ." "Yes! Toward the middle of the month, I settled on 30 seconds to be at round 5 in a game was fast and if the player hit around that mark, I would be nice and give the green. If it took longer than that, they got the red. . ."

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Supplementary Table 3 -Qualitative vs. quantitative analysis of strategies Classifications for all 94 players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 10 CC CC "I would always choose option 1 while my partner did the same, when they went to option 2 I followed. My goal was to make as many points for me as the other player. A few rounds I tried various strategies but always went back." "For the most part no." 11 threshold threshold "I cooperated on every round before defecting in Round 8." "In the first few games I would defect in round 10. Eventually I moved it up to round 9 as people caught on and then round 8. . ." 12 threshold CC "I played in the hopes that my partner would always choose Option 1. I saw it as such. . ." "Somewhere around the middle, I did start choosing Option 2 in Round 9 (and even Round 8 in some cases). . . by the end, I only chose Option 2 in response to a partner choosing Option 2. " 13 threshold threshold "For the first two days, I tried to defect on round 10 to get maximum money. . ." "But I noticed that most players were doing this. So after day 2, I always defected on round 9. . . for the last two days, I started defecting on round 8, to get maximum points." 14 threshold N/A "At first I tried to be as fair as possible so both my partner and I could maximize our earnings." "My strategy changed as more participant's became greedy. . . After a while, most players started defecting in the final round of each game." 15 threshold threshold "When I first started playing my strategy was to co-operate. . . shortly into the first game someone chose Choice 2 and therefore I only got 1 point and I was mad. For several sessions I decided I would just always make choice 2... Finally I decided to mostly cooperate and then around Round 7 to make the choice that would get me more points." ". . . I changed from always making choice 2 to mostly cooperating is that I thought I would make more money." 16 threshold threshold "Each day I would start off trying to cooperate to the fullest. After a few rounds I would switch to using a 2 on either round 8 or 9. . . If the user continued to use 1 I would follow up with a 1 after the test to reward the others cooperation, knowing that the user would probably enter 2 for the remaining rounds. . ." "Mostly the only change from above was moving from round 9 to 8 because 2 seemed to come up more often before round 10." 17 threshold threshold "I wanted to do what I could to get the most points for myself in the end. I chose choice 1 until the the 8th round, then I did choice 2." "In the beginning, my strategy was to just stay with choice 1 throughout the whole game, however people started doing choice 2 so I did as well. " 18 threshold threshold "At first I decided to always play fair no matter what. I wanted things to be equal as much as possible. Eventually however, I changed my strategy a bit to protect myself. . . I decided that it would be best to defect after round eighteen. . ." "At first i tried to use the first choice as much as possible, but after others defected sooner I also had too as well in order to keep things equal. . . I then decided that I needed to be proactive and assume that the person was going to defect after round eighteen. . . In a few cases it happened at round seventeen, but I did not change my strategy in this case even though it happened a few times. I felt that overall I would lose money if I changed my strategy to this round so I did not." 19 threshold threshold "I chose option 1 on round 1-8, and option 2 on 9 & 10 of each game." "Yes, I started out choosing option 2 only on the last round of each game, but later started choosing option 2 on rounds 9 & 10 when the other players began choosing option 2 more often on the last round." Continued on next page Supplementary Table 3 -Qualitative vs. quantitative analysis of strategies Classifications for all 94 players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 20 threshold threshold "Pretty much stuck with the plan to choose '1' throughout most of the game, then switch to '2' towards the end." "In the beginning, I'd alternated between 1 and 2 for whatever reason, but eventually figured that one the opponent had stuck with 2, there wasn't any real reason for me to choose 1 unless I wanted to give him/her free points." 21 threshold threshold "I tried to maximize my payout, assuming my partner would be doing the same, choosing one was beneficial to us both." "i began to defect in the later rounds when I noticed that others were doing do in order to minimize the loss." 22 CC CC "I just tried to be as far as possible and select 1 every time. I did this until the other player selected 2 and then I would start choosing that." "It didn't really change over the course of the study. 26 threshold threshold "i tried to keep the scores even, eventually trying to sneak in a few more once the other person thought i would pick the same number again" "i altered the round in which i chose to change numbers" 27 threshold threshold "I would try to cooperate (action 1), but then realized most people would pick option 2 at the end, so I would typically select 2 for the last two rounds." "I originally just picked all 1s as I thought everyone getting 50 per round was better than getting less than 50." players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses. "My strategy initially was to choose option 1 most of the time and then choose option 2 for the last two rounds but eventually I did option 1 the entire time unless the other person wasn't co-operating. " 38 threshold CC "I wanted to make sure it was fair, so I chose 1 always, unless someone chose 2. If I was being shorted by people picking 2 near the end, I'd chose 2 near the end against others and try to even it out by picking 1 if they didn't also pick 2 next round." "My strategy stayed the same, pick 1 unless given a reason not to. Maximize earnings for both parties." 39 threshold threshold "As it soon became apparent that all players understood cooperation will maximize payoff, I went along with the flow and selected option 1 up until the last round. If players appeared to be "playing" me (eg varying the times between choices) I would be more likely to select choice 2 in an earlier round. . ." "After i saw that timing variation in clicking, or just super-fast clicking, often coincided with players becoming uncooperative early, I tried to get ahead of them by clicking choice 2 earlier than planned." 40 CC threshold "At first, I chose for both me and the other player to get five points each round. I then thought hmm, maybe I can make a little more, so the last round I would make it so I would get 7 and the other would get 1. But eventually others started doing the same thing. . . So I then started trying to get 7 on the round 9 and then 3 on round 10. But I had a theory that this would overall cause a decrease in amount made. . . So I figured I might as well try to get others to adopt a better strategy. . . and more people started going with 5 and 5 all the way through. But alot were still trying to get that 7 at the end, so I chose towards the end to choose option 2 on round nine so I would either get 3 or 7 points. If I got 7, I would give the other player 7 on the next round assuming they chose option 2 on round ten. If I got 3, I would continue with option 2 so we would both 3. . ." "explained above" Continued on next page Supplementary Table 3 -Qualitative vs. quantitative analysis of strategies Classifications for all 94 players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 41 threshold threshold "Most of the time, I tried to select the first option. . . However, once in a while I would pick option 2 near the end to try to get the extra 6 points for a better payoff. I didn't want to do that too often though because I felt guilty as it wasn't fair to the other player." "Sometimes I did change strategies to try to get back the points I may have lost because the other player "got me" with the second option more than once, before I changed to option 2. I would try to keep the options fair by choosing option 1, but sometimes the other player would start off with option 2 and I would try to get them back to option 1. . ." 42 threshold threshold "I began by finding the general idea of how the group might play on the first day and seeing that mostly everyone would go 1's throughout except for maybe on 10 but not often at all. As the experiment progressed more people would start going 2 on 10. . . So as more people went 2 on 10 I decided that I would at least try to protect myself from getting 46 total points by splitting 2's on 10 by going 2 on 9 as well. . . However this became a trend and typically people would now always go 2 on rounds 9 and 10. I felt going beyond this was idiotic because in the end to continue in this fashion you are jeopardizing the whole groups pay. I felt comfortable either going 1 for all or 2 on 9 or 8 sometimes. . ." "See above answer." 43 threshold threshold "I started off trying to be fair and play equally. Knowing that we were playing the same participants every day, I tried to learn what patterns others were playing so I could adjust my play to benefit me but still be fair." ". . . When others would choose to take it all the last round, I started doing that also, choosing option 2 for tenth round only. . . Then I kept getting others who would start choosing 2 for the 9th & 10th rounds, so I did as well. For most of the month, I played choice 1 for the first 8 rounds then choice 2 for the last two rounds. . . This last 4-5 games, I ended up choosing option 2 for round 7 as well. I changed when others started taking more in earlier rounds." 44 threshold threshold "Early on in the study and early on during most individual days, I went with Choice 1 because I was attempting to keep things equal for both people. As time went on, I started to defect in order to play defense for myself. . . I started defecting around round 9 for most of the study and around round 8 at some points toward the end of the study." "Yes, my strategy changed from keeping things equal to defecting earlier and earlier to protect my earnings. It was not a fool proof strategy. . ."

CC CC
"I chose to mostly cooperate -I wanted to maximize payment for myself and the other player. Going into the games, I figured I would mostly cooperate and then deflect as others deflected." "It stayed mostly the same, I cooperated more than I thought I would. I guess I kind of hoped it would encourage others to continue to cooperate more as well." 46 CC CC "I tried to get the best outcome for me and the other person, which was by picking option one. However, if they tried to pull the best option in their favor, I would switch to option two so I wouldn't be left out in earnings." "No, I kept the same strategy the entire time." 47 threshold threshold "to cooperate as much as possible, until the end for my advantage" "when others caught on, I had to start switching sooner" Continued on next page Supplementary Table 3 -Qualitative vs. quantitative analysis of strategies Classifications for all 94 players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 48 threshold threshold "Well, I figured out that the only way to gain any extra money was to hit choice 2 at the very end (10th round). . . you're only going to be able to get that 2 in there once before they start hitting 2 also. . . So, I chose one every time except for the last round, UNLESS my partner starting choosing 2 earlier, then I chose 2 as well to protect myself." "I fiddled around with it a little bit the first week, but I settled on my strategy after that and kept it going straight through." 49 CC CC "Cooperating with the other player so I could at least gain some points." "For the most part, it changed toward round 8 and 9 and 10. Players were more inclined to give themselves more versus sharing." 50 threshold threshold "I eventually settled on choosing 2 for the final three rounds. Toward the end of the study, many people were choosing 2 on the final two rounds. I chose to press 2 one round before most people. . ." "My original strategy was to only press 2 on the tenth round when most people were choosing all 1. As the game progressed, more and more people were choosing 2 for the final round and I changed my strategy to compensate. I then started choosing 2 for the final two rounds in order to maximize my points. Toward the end of the study many other people were utilizing the same strategy, so I started pressing 2 for the final three rounds." 51 CC CC "I made Choice 1 until I saw the other person making Choice 2, and then I matched them for the remaining rounds." "In the first day of the game, I made Choice 2 at the end of one of the rounds to get extra money. I felt really guilty about doing this and decided it wasn't worth the emotional turmoil for me! So I continued by always making Choice 1 and only ever reacting to other greedy players once they made Choice 2." 52 threshold threshold "I thought choosing choice 1 for the first and majority of the beginning rounds would allow both me and the other person to earn more stably. Towards the ending rounds, I would often choose choice 2 at rounds such as 8, 9, or 10 to avoid ending with less points. . . If I missed out on a round, I would have also chosen choice 2 more often to make up for the points." "I don't think it really changed over the course of the study. There were slight adjustments depending on how previous players acted but I don't think they were significant." 53 threshold N/A "When i began i initially chose to defect, and would do so for a while. But then i realized that was not a fair strategy and reversed when i would defect." "It solidified over a couple of days and stuck to it as it was reaping the most benefits." 54 CC threshold "I started out by trying to be cooperative. . . I was concerned that the more I defected, the more mistrust would seep into the game and the worse everyone would do (though my concern was with my own results, not others'). . . I was willing to lose a few pennies each game if it meant people cooperated for 8 or 9 rounds at least. . . However, after weeks of feeling like I was being taken advantage of by people who defected in round 8 or 9, I started to defect more. . . the change in motivation here was to protect myself, not to be greedy and steal from others. Had I KNOWN others would cooperate, I would have done that. . ." ". . . in the last week I was tired of being taken advantage of in round 8 or 9, and so I started defecting in round 9 or 10 in a lot of the games. I didn't WANT to punish someone who was playing cooperatively, but I was very tired of being defected on when I was willing to be cooperative. My desire to be cooperative eventually was overcome by my desire not to be a sucker." 55 threshold threshold "None in particular. I started out choosing 1, seen others choosing 2 on Round 9 and started doing that." "I was choosing one a lot more in the end."

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Supplementary Table 3 -Qualitative vs. quantitative analysis of strategies Classifications for all 94 players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 56 CC CC "I always chose to cooperate, except when my partner chose to defect I also chose to defect for the remaining games." "no, the same strategies" 57 threshold threshold " I learned it was best to choose option 1 for the 1st 8 or 9 and then spring for choice 2 at the end, normally the last 1 or 2 games. That way they thought I was being cooperative and then I'd surprise them sometimes. . ." "Yes. When I 1st started playing I always went for what I thought would earn me a higher bonus (choice 2) right off the bat. I soon learned it was best to save that option for the last 1 or 2 games in each round and instead play choice 1 for the 1st 8 or 9 and then spring for choice 2 at the end. " 58 threshold threshold "My goal every time was to maximize my earnings. I also wanted the other person to do well but there was no way for me to know what they were going to do. Anytime I chose to defect it was only to protect myself, not to "steal" money or take advantage of the other player. . . Some players defected earlier and that was always a terrible choice, especially against me as I would then defect every round after no matter what." "At first I always wanted to cooperate but I then realized that defected in round 10 had no consequences. But after a while I kept getting burned in round 9 so I then started to defect in that round as well. Then the same thing kept happening in round 8 so again I started to defect. . ." 59 threshold threshold "I would try and chose the best option for the most points for both but at times i would change the last 2 rounds" "I foloowed the strategy that i would chose option 1 for the first 8 rounds and the last 2 rounds i would chsoe option 2" 60 CC CC "The best option for both parties was to cooperate, thus I chose option 1 to start with and only switched when the other party chose option 2. . ." "No, again, best bet for both parties was option 1, saw no reason to change unless the other player chose option 2." 61 threshold threshold "I selected choice 1 for the first 7 rounds, then chose choice 2 for the 8th round. If my opponent also selected choice 2 for the 8th round, then I would select choice 2 for the remaining rounds because I could see that they were trying to beat me. If my opponent chose choice 1 for the 8th round, I would choose choice 1 for the 9th round to let them win that round for not trying to trick me and then possibly even out again. (7/1, 1/7). I would choose choice 2 for round 10." "I originally selected choice 1 for all rounds until I saw that some of my opponents switched up, which made me end up with less." 62 CC CC "I wanted to continue to cooperate as long as possible. That would maximize the common payout" "Every now and then I defected, but I didn't really have a strategy other than doing it late in a round" 63 threshold threshold "...I started then selecting 1 all the way up until round 10. After a few days people caught on, so I had to start doing "2" in round 9. . ." "It changed a bit as I described previously, but after a week, the strategy was basically the same. " 64 CC CC "I tried to cooperate until I grew frustrated with people not doing so. I didn't see a point in choosing 2 before round 9. I switched back and forth depending on how it was going and how angry I was getting with people." "I didn't really change my strategy over the course of the study, I would change it during each day depending on how I was feeling about how the game was going. " 65 threshold CC "Ideally I wanted both my partner and I to pick choice 1 every time. Once I saw someone pick choice 2, I followed so I would still get 3 points." "Same strategy" 66 threshold threshold "I tried to cooperate, but after seeing people defect (most often in the last 2 rounds) I started defecting myself in the rounds 9 and 10 most of the time." "I started off just cooperating all the time as I figured it was fairest to try to give all of us the same payoff. Eventually I started defecting in the last two rounds as I saw more players doing this and it maximized my earnings." Continued on next page Supplementary Table 3 -Qualitative vs. quantitative analysis of strategies Classifications for all 94 players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses. players who completed the experiment as well as their responses to the two strategy-related questions in Section . Inferred Strategy denotes our analysis from the data, and Qualitative Strategy refers to our independent classification from the textual response. Note that in participants' responses, "Choice 1" (colored green) and "Choice 2" (colored red) refer to cooperate and defect, respectively, although they were not labeled as such in the experiment interface. We did explain cooperation and defection in debriefing, hence participants referred to these labels or colors interchangeably in their responses.

# Inferred Strategy
Qualitative Strategy ...did you follow any particular plan or strategy?
...did it change over the course of the experiment? 77 threshold threshold "I tended to select option 1 every round until the other player chose option 2 for 2 or 3 consecutive games. after that I defected in round 9 to try to get a jump on the other player." "It did change significantly. I figured it was in both players' best interest to choose option 1 in every round. I tried to stick to that for a while, but found that people didn't see it the same way. . . In the end, I would choose #1 all the way until people started defecting in round 9 or 10. At that point I would defect in round 9 and if the other player chose option 1 in round 9, I would choose 1 in round 10 so their points and mine would be equal." 78 threshold threshold "I tried to cooperate on the first nine rounds, assuming the person cooperated in previous rounds. Then, I would not cooperate on the last round -I felt this was the best way to play." "Eventually, I chose more and more to not cooperate on the second to last round, as many people were doing the same to me. . . However, I am not sure if this actually made me more money, but if I continued to cooperate when others did not, I feel like it would have cost me money." 79 threshold threshold "I started off early in the month with the strategy of trying to cooperate until the very last minute (round 9 or 10 or so is when I would choose option 2). However, I gradually noticed more and more people going for the 9th and 10th rounds, so I decided to usually choose option 2 directly after the 7th round. "In the beginning I chose a variety of numbers in each turn. Then I started choosing 2 on the 10th turn. I changed this strategy because I noticed more and more people choosing 2 before the 10th turn. " 84 CC CC "I always cooperated until the other person didn't." "I stuck to the same strategy throughout. . ." 85 CC CC "I pretty much always went with choice one. . . If everyone with with choice two, then everyone actually earns far less than they do if they cooperate. . ." "The strategy didn't really change for me. I did choice one as long as the other person did. Once they did choice two, I immediately did it to counter them. . ." 86 CC CC "I chose to cooperate until my partner did not. After they didn't, I didn't anymore either so as to not reward them for choosing 2." "I didn't change mine at all. I knew that choosing 1 more would benefit us both, so I chose that every time until my partner chose 2" Continued on next page

Experiment Instructions
Welcome This HIT will grant you a qualification for a month-long research study consisting of 20 sessions where you will play a game with other workers. Each session will start at the same time every weekday (Monday through Friday) and take about 20-30 minutes, and the sessions will take place over the course of about 4 weeks. We expect the experiment to start the week of August 3, 2015 and run at least through August 28, 2015.
If you choose to participate in the study, you will need to be present for every session. If you miss more than 2 sessions, you will no longer be allowed to participate. Please only agree to participate if you can make a commitment to be present for all 4 weeks.
Because this is a research project, we also ask that you please do not discuss the study in online forums or chat rooms while participating.
In this HIT, we will ask about your availability and schedule the sessions at a time when the most workers are available. If you agree to participate, we will contact you when the study begins and specify the time that you should arrive on each day. Since the study involves interacting with other workers in real-time, it is important that on each day you arrive on time and start the HIT immediately.
Once you read these instructions, you will see a short quiz that tests your understanding of the rules of the game (as described below). If you fail the quiz twice, you will not be able to participate in the study.
The Game In each session you will play a sequence of up to 20 games where you will be randomly paired with another player.
Each game consists of a sequence of 10 rounds. Each round, you have a choice between two different actions (Choice 1 and Choice 2). You will have one minute to make your decision. After both you and your partner make a decision, you will each receive a certain number of points. This table shows how many points you and your partner will earn based on your choices: Choice 1 (Partner) Choice 2 (Partner) Choice 1 (You) 5, 5 1, 7 Choice 2 (You) 7, 1 3, 3 In each cell, the first number is how many points you will receive, and the second how many points your partner will receive. In other words: • If both you and your partner select Choice 1, you each earn 5 points.
• If you select Choice 1 and your partner selects Choice 2, you earn 1 point and your partner earns 7 points. • If you select Choice 2 and your partner selects Choice 1, you earn 7 points and your partner earns 1 point. • If both you and your partner select Choice 2, you each earn 3 points.
Each game ends after 10 rounds, and you will be randomly matched with another partner for the next game. Once you have completed 20 games (possibly fewer, given the availability of other players), you will be able to submit the HIT.
You will then return the next day to complete another session, and so on for 20 sessions over the course of 4 weeks.
Payment You will receive a base payment of 10 cents for each of the 20 sessions. For each session, you will also earn a bonus based on the total number of points you receive. We will convert your score to dollars at the rate of 2 points = 1 cent. We expect this will allow you to earn a minimum of $9.00 per hour. You will receive an additional bonus payment of $20 if you are still participating at the end of the 20 sessions. This bonus will be at least 20% of your earnings.
In total, you will be able to earn a minimum of $80.00 (including the additional bonus payment) through fully participating in this study.