Some dogs can find the payoff-dominant outcome in the Assurance game

Summary Studies on coordination often present animals with the choice of either cooperating or remaining inactive; however, in nature, animals may also choose to act alone. This can be modeled with the Assurance game, an economic game that has recently been used to explore decision-making in primates. We investigated whether dyads of pet dogs coordinate in the Assurance game. Pairs were presented with two alternatives: they could individually solve an apparatus baited with a low-value reward (Hare) or they could coordinate to solve a cooperative apparatus baited with a high-value reward for each dog (Stag). All individuals matched their partner’s choices, but after controlling for side bias, only four out of eleven dyads consistently coordinated on the payoff-dominant strategy (Stag-Stag). Thus, some dogs are capable of finding coordinated outcomes, as do primates, at least when their partner’s actions are visible and coordination results in the biggest payoff for both individuals.


INTRODUCTION
Coordination among group-living animals often occurs in cooperative contexts (e.g., hunting, parental care), in which coordination benefits all participants. 1When subjects' objectives are aligned, coordination may arise due to subjects independently acting toward the same goal (e.g., by-product mutualism 2 ), without understanding the cooperative situation. 3Thus, a key question is to what extent animals consider their partner's actions in the task and use that knowledge to adjust their own actions accordingly. 4mong animals, humans' unique flexibility in cooperating with others is thought to be grounded in their ability to recognize the role and intentions of their partners.Therefore, studying the degree to which other animals recognize the consequences and the importance of their partner's decisions during coordination is crucial to shed light on the evolutionary origins of human cooperation.
Most research exploring how non-human animals coordinate actions with each other has relied on the cooperative pulling/pushing paradigm.In this paradigm, two or more individuals must simultaneously pull handles/ropes, [5][6][7][8][9] or press buttons, [10][11][12] to gain access to food rewards for both individuals.Thanks to these studies, we know that some species understand at minimum that they need a partner present to solve the task. 13However, one disadvantage of the cooperative pulling/pushing tasks is that there is only one option to access the rewards: pulling/pushing at the same time as their partner.If subjects fail to do that, they obtain nothing.This does not represent the complexity of options that animals have in nature, wherein animals frequently face problems that can be solved either individually or cooperatively.For instance, an animal might choose to participate in group-hunting to obtain a high-quality food or they may prefer to avoid the risk that comes from working with others (e.g., their partner can monopolize the rewards 14,15 ) and instead choose to forage alone for lower-quality food.To explore whether subjects understand the role of their partners in such scenarios, a different task is required.Economic games offer a promising approach that overcomes the limitations of previous paradigms to model a wider range of situations.
Games derived from experimental economics are highly structured tasks that represent complex social situations in the form of simple, usually dichotomous, choices and in which outcomes are dependent on the combination of the participants' choices. 16Economic games have been historically used to study the adaptative function and evolution of cooperation. 17However, in recent times they have also proven fruitful for uncovering the cognitive mechanisms, particularly from a comparative perspective, due to the simplicity and flexibility of these games. 18Game's choices can be implemented in diverse ways and adapted to each species, using, for instance, tokens, 19 trays, 20 or computer icons. 21Specifically, the decision to hunt together for a high-quality reward or forage alone for a lesser reward can be modeled using the Assurance game.
In the Assurance game, or Stag Hunt game, two individuals must choose one of two options: Stag or Hare.The payoff matrices for the Assurance game differ across disciplines and studies; however, they maintain key features that make the game a coordination game.It is Comparing the proportion of each possible outcome (Stag-Stag, Hare-Hare, Hare-Sag, and Stag-Hare) with chance level (25%) by means of chi-square goodness-of-fit test, we found that all dyad's performances deviated from chance (see Figure 2; Table S3; Figures S6-S8).By inspecting the standardized residuals of each outcome 55 (significant at p < 0.01 for +/À 2.58), we determined the most frequent outcome for each dyad and session and whether it deviated from chance.Four of the dyads (dyads 3, 7, 10, and 11) consistently coordinated on Stag in both sessions, whereas the outcomes of the other dyads could be explained by at least one of the members of the dyad showing an individual preference for one side of the room or, in the case of dyad 4, perhaps tolerance issues.Specifically, six dyads changed their preference when we changed the position of the Hare and the Stag tables in the second session (i.e., in both sessions they always chose the same side, independently of the table that was placed there): four of them showed a significant preference for  S4).

Do dogs flexibly adjust to their partner's choices in the Assurance game?
In the S2 model, we found that Subject 2 was more likely to choose Stag when S1 also made that choice (full-null model comparison: c2 = 23.31,df = 4, p < 0.01; estimate for the effect of S1's choice = 5.947, SE = 0.770, p < 0.001; see Figure 3A).None of the interactions between the predictor (S1's choice) and the control variables was significant (see Table S5), showing that the effect of S1's choice on S2's choice did not depend on trial number, or whether the previous trial resulted in a reward, or on dyad type (i.e., it was the same in dyads that showed little variability in their responses-mostly coordinated on Stag-and the rest of the dyads).In turn, the S1 model revealed that Subject 1 was more likely to choose Stag if S2 had chosen Stag in the previous trial (full-null model comparison: c2 = 13.97,df = 3, p = 0.003; estimate for the effect of S1's choice = 5.10, SE = 1.24, p = 0.045; see Figure 3B).This effect did not depend on trial number or dyad type (none of the interactions in the model were significant, see Table S6).We did find a main effect of dyad type (estimate = 6.22,SE = 2.13, p < 0.001), meaning that S1 chose Stag more often in dyads that consistently coordinated on Stag than in the other dyads.

Do dogs change their tolerance toward their partners after successful coordination in the Assurance game?
The interaction between HVR consumed and condition (training session/Assurance game) was significant (Tolerance model, full-null model comparison: c2 = 4.19, df = 1, p = 0.041), indicating that dogs spent more time cofeeding if they had eaten more HVR before the tolerance test (that is, more coordination on Stag resulted in more time cofeeding in the tolerance tests), but only when that food was obtained in the Assurance game (see supplemental information, Figure S9).Regardless, we found that the estimate of this effect was not stable (see supplemental information, Table S7), which indicates that the effect might be limited to some dyads.Visual inspection of the results revealed that only two dyads showed an increase in cofeeding after more coordination in the Assurance game (dyads 1 and 3, see Figure S10).Overall, the effect of the interaction that we found is not reliable, which may be due to our small sample size, and we might find a different effect in either direction (smaller or stronger) with a different sample.

DISCUSSION
Comparative work using the Assurance game in primates showed that at least some pairs of all species were capable of coordinating on mutually beneficial outcomes, but the mechanism underlying coordination varied across species and even groups. 13,18,56In the current study, we demonstrated that some pet dog dyads also coordinated their choices on the payoff-dominant NE, while the remaining dyads changed their preference depending on the session.Importantly, we found that dogs adjusted their choices based upon their partner's choices, even when they did not coordinate on Stag.Whereas this could be achieved by simple mechanisms, such as matching (a mechanism seen in some primates), we cannot rule out that they understood their partner's role.A more in-depth analysis of our findings is presented in the following section.
Not every pair coordinated: of eleven dyads of dogs, four of them coordinated their choices on Stag, the payoff-dominant NE, in both sessions, which maximized both dogs' rewards.Subjects also adjusted their choices around their partners; when we explored how the choices of the partners affected each other, we found that S2 was more likely to choose Stag when S1 chose Stag, and S1 was also more likely to choose Stag if S2 had chosen Stag in the previous trial.This is reminiscent of macaques and capuchins in Prisoner's dilemmas, who also change their choices based on those their partners make. 31,57The model results were the same for the dyads that found the payoff-dominant NE and for the rest of the dyads, suggesting that they pay attention to one another's choices no matter what the outcome/strategy they choose.
These findings stand in contrast with previous research in which pairs of dogs failed in a cooperative pulling task 6 and showed only a moderate improvement after extensive training. 51The difference is striking because the apparatus was the same as our Stag table; in those studies, 6,51 dogs were required to pull a rope at the same time on the same table to get the food.There was, however, one key difference; their sample was composed of pack-living dogs, and, as they argued, lack of tolerance, rather than cognitive limitations, can explain why dogs were reluctant to act simultaneously.We pre-selected tolerant dyads by limiting our sample to pet dog pairs living in the same household, a selection bias that undoubtedly influenced our results (cf. 58).This may be why, contrary to studies suggesting that affiliation and tolerance are key to coordination, 9,15,59 we found no relationship between tolerance around food sources and the proportion of Stag-Stag choices of each dyad.Moreover, two elements of our setup might have reduced the necessity for tolerance.First, owners were in the room for the whole duration of the experiment, which presumably helped to inhibit conflicts; and second, dogs were separated by a fence, preventing physical contact between them.In this regard, we observed one aggressive interaction in dyad 4, which appeared to lead to uncoordinated choices.This is in line with previous work that has found that when conflicts arise, dogs use an avoidance strategy that can easily lead to the breakdown of cooperation. 6,53Thus, future work with more variable relationship quality might find an effect.
Six dyads preferentially choose Stag-Stag in one session and Hare-Hare in the other session, which indicates either a side bias in both individuals (both prefer the same side of the room, without attending to their partner's choices) or that one of the individuals was side biased and the other individual followed them.Indeed, if one of the players in the Assurance game invariably chose the same option, the best-paying possibility for the second player would be to make the same choice.The dogs do appear to be taking each other's choices into account; our analyses revealed that S1 was more likely to choose Hare if S2 chose Hare (instead of Stag) in the previous trial.
When considering all the aforementioned factors, there are two potential (and not mutually exclusive) strategies in play.First, the four dyads that found the payoff-dominant NE seem to understand the payoff matrix, showing a majority of Stag-Stag choices (although sometimes, dogs would also choose Hare-Hare).Second was matching, which does not always yield the highest payoff, but can be the best solution with a partner who does not understand the task or shows a side bias.This strategy has been seen in some primates; capuchins only coordinated when they could see their partner's choices, suggesting matching, 21,24 and in one study, chimpanzees who did not have extensive testing experience used matching (or showed no strategy). 24In another study, 60 macaques played a version of Bach-or-Stravinsky in which the partner's actions were always visible.In this game, two individuals received a better payoff if their choices were coordinated in either of two options.However, one coordination option provided a higher reward for one individual, whereas the other option provided a higher reward for the second individual.Some pairs of macaques consistently coordinated on just one of the two options, even when the most payoff-equalizing strategy would have been to alternate which option they coordinated on (as most human pairs did in the study), whereas other macaque pairs found an efficient and payoff-equalizing strategy by coordinating on the same side.This evidence, together with our results, suggests that non-human animals tend to rely on matching mechanisms when they can see their partner's choice.
In fact, imitation is believed to play a crucial role in the evolution of cooperation by shaping behavioral strategies such as Tit-for-Tat, in which subjects imitate their partners' previous behavior (e.g., whether they receive help from a social partner 61 ).Imitation can enable seemingly coordinated behaviors without a real understanding of the payoff matrix when individuals copy the other's actions, for instance, to obtain a food reward.Future studies should explore whether dogs can maintain coordination when the use of a matching strategy is challenged, such as when their partner's choices are not visible, or when the choices of Stag and Hare involve different actions for each subject.
Although we cannot answer the question, it is useful to speculate on what mechanisms may be underlying the dogs' choices.Dogs' matching strategy could have emerged through basic mechanisms such as local enhancement 62 or stimulus enhancement. 63][66] Whereas in these situations, in which subjects have access to the partner's actions, low-level cues might be sufficient to succeed; we cannot exclude that they also consider other aspects of the social situation when making decisions.In this regard, we predicted that if dogs understood their partner's role in the HVR obtained in the Assurance game, the amount of time that they spent cofeeding in the tolerance test would depend on the number of Stag-Stag choices in the Assurance game.That is exactly what our model revealed.Unfortunately, those results, although significant, were very unreliable.
In 4 out of 11 dyads, dogs were able to behaviorally coordinate to obtain a mutually beneficial reward.However, studies in primates suggest higher levels of coordination, such as chimpanzees (8 individuals/12 pairs, average proportion of Stag-Stag G se = 0.91 G 0.06), 29 rhesus macaques (8 individuals/5 pairs, average proportion of Stag-Stag G se = 0.81 G 0.09), 21 and capuchin monkeys (12 individuals/6 pairs, average proportion of Stag-Stag G se = 0.83 G 0.13), 31 but not squirrel monkeys (10 individuals/5 pairs, average proportion of Stag-Stag Gse = 0.33 G 0.13), 23 but there are several caveats to consider.First, because our subjects were brought into the laboratory, we were limited in how often we could test them, thus they received only two sessions of 40 trials each (whereas some primates have received up to 10 sessions of 60 trials).With more experience, more dyads might have overcome their side bias and found the payoff-dominant NE.Indeed, the proportion of dog dyads that found the payoff-dominant NE is similar, if not higher, than in primates experiencing the task for the first time.For example, when Brosnan and colleages 24 first tested chimpanzees and capuchin monkeys, only one out of six capuchin monkey dyads and two out of fourteen chimpanzee dyads found the payoff-dominant NE in the first 10 sessions (with 30 trials per session), with the remaining pairs matching their partner's choices or showing no identifiable strategy.With more exposure to the game, the same capuchin monkeys coordinated in the payoff-dominant NE. 21,31,67 Thus, even when dogs in our study were tested with a considerably lower number of sessions in comparison with other species, four dyads (36% of our sample) were able to find the payoff-dominant NE.
We tested dogs for the first time in an economic game, aiming to break new ground and propel new research avenues.We encourage other researchers to extend the use of economic games to different populations of dogs, such as free-ranging and pack-raised dogs or dog-dog and dog-human dyads with different degrees of familiarity.This would allow us to better disentangle the effect of social relationships between partners from their understanding of the task contingencies.Additionally, it is yet to be tested whether dogs could find the NE in anti-coordination games that cannot be solved using matching, as players benefit from playing the opposite strategy of their opponents.For example, in the Hawk Dove game, often used in the context of producer-scrounger dynamics and social learning, 68,69 players achieve the highest payoff if they defect while their partner chooses cooperation, but if both players defect, that results in the highest cost for both of them.Finally, more research is needed to explore to which extent animals understand the role of their partners when playing economic games.Ideally, that research should be part of a research program that systematically compares, using equivalent procedures, whether and how animals across taxa coordinate and make decisions. 70,71Ultimately, this knowledge will shed light on the evolutionary trajectory of social decision-making. 72

Limitations of the study
A crucial constraint in our study is the limited number of dyads that we were able to test due to constraints in recruiting volunteers who had two dogs that passed criterion and were willing to bring them repeatedly to the laboratory.All the pairs were similar in age (all adults), could not mate (for the mixed-sex dyads, no female was in heat and at least one of the two members was neutered), and all dyads were formed by dogs living in the same households and with a tolerant relationship outside the testing environment.However, although we accounted for dyad identity in our model, our sample size did not allow us to fit more complex models encompassing factors such as dyad composition and other potentially influential variables such as subject's sex.Nonetheless, we did account for variability between dyads by incorporating dyad identity as a random intercept in the models.Perhaps future studies will be able to ask these questions with a larger sample.
Furthermore, in the Assurance game, the Stag and Hare's values are typically the same for both participants unless the authors are explicitly testing the role of different values in affecting responses. 67In this study, we had to use food individually selected for each dog due to dietary and time limitations.Thus, out of 11 pairs, for three of them the LVR was a different food within a dyad, and for two pairs both the HVR and LVR were different within the dyad.Although this could have influenced their decisions (i.e., by modifying the perceived payoff matrix, for example, if a player considers the Hare of the other player as valuable as their own Stag), our data suggest that it did not.Considering both HVR and LVR, one of the four pairs that coordinated had different LVR and HVR; considering LVR, two of the four pairs that coordinated had different LVR, and three out of seven that did not coordinate had different LVR.Comparing the dyads that coordinated and the ones that did not, the variation in the proportions of dyads that have the same vs.different types of food does not suggest a big impact.However, our sample size is small to give a clear answer, and future research will hopefully be able to address this issue when considering coordination in dogs.
Finally, our study was focused on the proximate mechanisms of coordination, and future studies should address how those have been selected by natural selection (e.g., kin selection, 73 direct or generalized reciprocity, 74 or by-product mutualism 2 ).
Data used to fit models reported in this paper have been deposited on OSF and are publicly available as of the date of publication.DOI listed in the key resources table.
All original code has been deposited at OSF and is publicly available as of the date of publication.DOI listed in the key resources table.Any additional information required to reanalyse the data reported in this paper is available from the lead contact upon request.

EXPERIMENTAL MODELS AND SUBJECT DETAILS Animals
We tested eleven dyads of pet dogs (13 females and 9 males, mean age GSD: 5.19 G 2.91 years) of varying breeds (see supplemental information, Table S1).Four additional dyads were unable to complete the training because one or both of the dogs lost interest in the task (3 dyads) or because the owner stopped participation (1 dyad).Dyads were formed by dogs living in the same household for at least 6 months that did not show aggression towards each other.Three further dogs participated as stooges in the training.The study was conducted at the Clever Dog Lab at the University of Veterinary Medicine Vienna in an empty test room (approx.6 m 3 2 m).All dogs participated in the different phases of the study (preference test, training, tolerance tests and Assurance game) in the same order (see supplemental information, Figures S2 and S3).
the entire length of the rope out and the table could no longer be solved (if a dog chose Stag but their partner had chosen Hare).Dogs were not allowed to make a second choice.If, after pulling the rope in one table, the dog attempted to reach the other table, the experimenter approached that table and wound the rope inside the apparatus, out of the dog's reach.The trial ended once the two dogs had made a choice or after 40 seconds, at which point the owner and experimenter called the dogs back to the starting position.Then, the experimenter left S2 in the starting position and went to re-bait the apparatuses.The experimenter visited all the tables independently of whether they were empty or still baited after the previous trial, starting with a different table in each trial.After that, the experimenter returned to the starting position and a new trial began; this was repeated until all 40 trials were completed.

Tolerance test
To evaluate if coordination in the Assurance game affected the dogs' attitude towards their partners, we assessed whether the dyad's tolerance levels in a food context, measured as time feeding together on a food resource, changed after the Assurance game.For this reason, we conducted one tolerance test after each of the Assurance game sessions to determine whether dogs that coordinated more on Stag (measured as the amount of HVR that they ate in the Assurance game), were more willing to co-feed during the tolerance test.Even if that prediction was confirmed, that does not necessarily mean that dogs are changing their attitudes towards their partners because they understood their role in obtaining the HVR during the Assurance game.Instead, they may co-feed more merely because they are more satiated by the HVR eaten during the Assurance game or because they developed a positive association between the presence of the partner and the HVR.Those last two scenarios do not involve any understanding of the game.To account for this, we included three additional tolerance tests, conducted in three different days immediately after the training sessions.To control for the effect of the HVR that they receive during the experimental sessions, in these subsequent three sessions dogs were fed variable amounts of HVR (none, 20 or 40, order counterbalanced between dyads) before the tolerance tests (once the training was over, to avoid interfering with it).If dogs changed their attitudes towards their partners after successful coordination in the Assurance game, dogs co-feeding would be influenced by the amount of HVR eaten before the test in the Assurance game, but not by the amount of HVR eaten before the test in the training days.
In the tolerance tests, 54 dogs were presented with a single bowl filled with one cup of dry food.The bowl was covered with a cardboard box (see supplemental information, Figure S5), attached to a rope threaded through a hook in the ceiling, in a way that the experimenter could lift the box from a distance (1.5 m from the box), to avoid the potential interference of a human in close proximity.The experimenter lifted the box when both animals were within 10 cm of the box, allowing them to approach and eat the food.The test ended when there was no food left or when both dogs were more than one body length away from the bowl.

QUANTIFICATION AND STATISTICAL ANALYSIS
All tests were video-recorded for later coding.For each individual in every trial of the Assurance game, we coded the choice (Hare, Stag, or no choice), and whether S1 or S2 was the first one to move two steps towards the Stag or Hare table (see Data S1).A second person, blind to the aim of the study, coded 20% of the videos, revealing excellent consistency between coders (Intra-class correlation coefficient for co-feeding time = 0.953, Cohen's kappa for dog's choice and which subject moves first = 1).
Statistical analyses were done after excluding the trials in which one or both members of the dyad did not make a choice.Average proportion of missing trials per dyad was 0.04 G 0.11.We tested whether dyads' choices of each of the four possible outcomes (Stag-Stag, Hare-Hare, Hare-Stag, and Stag-Hare) in each session were different from chance.To do this we used chi-square goodness-of-fit and, as there were four possible outcomes, we set the chance level at 25%.Whenever the chi-square was significant (p < 0.05), we checked the standardized residuals to assess which of the four outcomes differed from chance.Standardized residuals of +/À 2.58 were considered statistically significant (p < 0.01). 55e explored which factors influenced whether dyads found the payoff-dominant NE (Stag-Stag) with a binomial Generalized Linear Mixed Model (GLMM), 77 the Stag-Stag model.Whether the dyad's choice was Stag-Stag in each trial was the response variable.To test if more tolerant dyads were more likely to choose Stag-Stag, we included the proportion of co-feeding in the tolerance tests before the Assurance game (one single measure derived from averaging their proportion of co-feeding across the first three tolerance tests).To test for learning effects, we included trial and session numbers as predictors in the model.Finally, to test for the effect of age, we included the S1 and S2's age as predictors.We also added the three-way interactions between trial number, session number, and the rest of the variables (i.e., trial x session x tolerance, trial x session x S1's age, trial x session x S2's age).
To assess whether the subjects adjusted their behaviour to each other, we ran two different binomial GLMMs.In the first one (S2 model), we tested whether S2's (the second dog to be released) choice of Stag or Hare was influenced by S1's (the first dog to be released) choice.In this model the choice of S2 was the response variable and S1's choice was used as predictor.We also included the fixed effects of trial, and whether S2 received a reward in the previous trial (to control for the possibility of dogs maintaining/changing their choices solely depending on whether they were previously rewarded for that choice).Additionally, as certain dyads consistently coordinated on Stag in both sessions, we were concerned that this lack of variability could influence the results.Thus, add the variable ''dyad type'' to the model.This variable was used to define two types of dyads: 1) dyads that coordinated on Stag in both sessions, and 2) other dyads (including side biased dyads and one dyad that coordinated on Stag in the first session and made uncoordinated choices in the second session).We also included all the twoway interactions between the predictor (S1's choice), and the control variables (rest of the variables in the model).
To explore whether S1 was adjusting their choices to S2's, we ran a GLMM testing whether S1's choice (response variable) was influenced by S2's choice in the previous trial (predictor).We used the S2's choice in the previous trial instead of the current trial because S1 was always the first one to choose (in our data, S1 never delayed, so S2 was always the first one to choose).However, S1's choice could take into account S2's choice in the previous trial (e.g., if in trial n-1, S2 chose Hare, this may encourage S1 to also choose Hare in trial n).We also included the fixed effects of trial number and dyad type, together with the two-way interactions between these variables and the predictor.In the S1 model we could not include whether S1 was rewarded in the previous trial because that variable was redundant with Subject's 2 choice in the previous trial (i.e., most of the trials in which S2 chose Stag resulted in a reward for S1 because they led to successful coordination).
Because S2 was released after S1, our models assumed that S2 could always see where S1 was heading before making its own choice.However, we notice that in a few trials S1 was not always the first one to move.Thus, we removed the 50 trials that did not meet that assumption from our sample before fitting the S1 and S2 models (in 8 trials that information was not available because of camera malfunction, in 4 trials both dogs moved virtually at the same time, and in 38 trials S2 started moving first).
Finally, we explored whether successful coordination in the payoff-dominant NE influenced the subject's behaviour towards their partner after the game.In the Tolerance model we used the proportion of time that dog dyads spent feeding together in each tolerance test as a response variable.For this model we used a zero-inflated beta GLMM (45.5% of the tolerance tests resulted in no co-feeding).We aimed to test whether the amount of high value reward (HVR) eaten before the tolerance test led to more tolerance (co-feeding) among the partners, but only if this HVR was obtained by coordinating in the Assurance game, in contrast with the days in which the HVR was given by the experimenter before the tolerance test (i.e., training days).For this reason, we included both the number of HVR eaten before the tolerance test and condition (whether it was a training or a testing day) in the model.We aimed to test for the significance of the interaction between these two variables.
All the GLMMs included dyad identity as a random intercept, and all the identifiable random slopes within dyad (see supplemental information and Table S2 for a detailed description of the model's construction).Additionally, to account for the variability in dyads sex composition, we included in all the models a random factor with S1 and S2 sex (i.e., four levels: malemale, malefemale, femalefemale, femalemale).We used a full-null model comparison approach, comparing the models through likelihood ratio tests 77 with models lacking the predictors but otherwise identical.
Statistical analyses were conducted in R 4.0.5. 78For the GLMMs we used the package ''lme4'' 79 whenever the response variable was dichotomous, and ''glmmTMB'' 80 when it was a proportion.
Hare-Hare in the first session and changed to Stag-Stag in the second session (dyads 1, 5, 8, and 9), and two of them chose Stag-Stag in the first session and switched their choice, showing a majority of Hare-Hare in the second session (dyads 2 and 6).Finally, dyad 4 coordinated on Stag in the first session and made uncoordinated choices in the second session, with most trials in which S1 chose Hare and S2 chose Stag.Importantly, uncoordinated choices in this dyad started after the only aggressive interaction that we observed during the Assurance game, in which S1 growled at S2. Inspecting different factors that could have influenced whether dyads coordinated on Stag, we found that Stag-Stag choices were not more likely to happen in the last trials or in the second session and that neither tolerance (cofeeding in the tolerance tests) nor S1 and S2's age have an effect on whether dogs coordinate in the payoff-dominant NE (Stag-Stag model, full-null model comparison: c2 = 10.41,df = 15, p = 0.79, see supplemental information, Table

Figure 1 .
Figure 1.Setup for the Assurance game (A-C) Haretable (A), Stag table (B), and starting position (C).In the game trials, subjects can choose whether they want to cooperate (Stag) or defect (Hare) by choosing whether to pull the rope from one or another sliding table.(C) The Stag table is on the left and the Hare table is on the right.

Figure 2 .
Figure 2. Dyads' performance in the Assurance game (A) 2D scatterplot showing the proportion of Stag-Stag choices by dyad (excluding trials in which either S1 or S2 did not make a choice), in session 1 (x axis) versus session 2 (y axis).Dyads that showed a majority of Stag-Stag choices in both sessions are shown in green.Dyads that showed a majority of choices of Stag in one session and Hare in the other session (side bias) are shown in purple.The dyad that coordinated on Stag in the first session and made uncoordinated choices in the second session (other) is shown in yellow.(B) Examples of dyads' performance in the Assurance game.Each dot represents S1's (black) or S2's (gray) choice in each trial.Black dots are bigger than gray dots, and thus, when choices overlap and the gray dot is on the top of the black dot, the graph shows the gray dot with a black ring around it.Blank spaces indicate trials in which the individual did not make any choice.For other dyads, see Figures S6-S8.

Figure 3 .
Figure 3. Relationship between S1 and S2's choices Proportion of Stag choices of S2 depending on S1's choice (A) and proportion of Stag choices of S1 depending on S2's choice in the previous trial (B) (11 dyads).Lines represent the fitted model for the effect of trial number and S1/S2 choices (blue lines represent the predicted response when the other individual choice is Hare; gray lines represent the predicted response if the other individual chooses Stag).Dots represent the proportion of Stag choices of S2 (left) and S1 (right) averaged by session, trial, and whether the other individual choice is Hare (circular points) or Stag (cross-shaped points).Shadowed area corresponds to 95% Wald confidence intervals.

table ( A
), Stag table (B), and starting position (C).In the game trials, subjects can choose whether they want to cooperate (Stag) or defect (Hare) by choosing whether to pull the rope from one or another sliding table.(C) The Stag table is on the left and the Hare table is on the right.