1. Introduction

Coordination problems occur widely in nature and across many domains of behavior. For example, in reproduction synchronizing courtship behaviors can influence mating success [1,2], in biparental care effective timing of the handover of duties between parents can increase offspring survival [3,4], in animal movement executing a specific collective escape response can improve a group’s chances of evading a predator [5], and in foraging the success of group hunts increases if the hunters are well-coordinated with each other [6].

Many coordination problems take the form of repeated multi-agent interactions where the same problem is encountered by varying subsets of a population (sometimes with the same members and sometimes with others) and are characterized by having more than one possible solution, which may be equally good. These repeated interactions can allow the population to converge on a specific solution if the individuals involved selectively and consistently adopt one of the possible alternatives. Following the seminal work of Lewis [7], we refer to such solutions as “conventions”: arbitrary and self-sustaining practices that emerge in a population and facilitate efficient solving of a specific coordination problem (see also [8] for a recent review). Conventions can, in turn, vary across populations since there may be multiple stable solutions to the coordination problem rather than a single “correct” or globally optimal solution – instead, which solution a population settles on may be determined by stochastic historical contingencies. For example, greeting behavior in humans can consist of shaking hands or bowing (where both parties are expected to perform the same action), and which manner a given population uses is a function of that population’s own unique history of inter-individual interactions. Similarly, driving conventions dictate whether motorists drive on the left or the right side of the road on a country-by-country basis, with either solution facilitating efficient and safe traffic flow as long as it is consistently adopted by the population at large.

While the term convention is sometimes used interchangeably with the term “norm”, several authors have drawn important distinctions, for example along the axis of normative expectations (where norms, but not conventions, are accompanied by expectations about what one “ought” to do, [9]) or the underlying problem structure and reward/punishment regime (with conventions emerging as solutions to coordination problems maintained at least in part through non-social rewards, whereas norms act as solutions to problems where there may be a conflict between self-interest and collective gain, often enforced via social rewards or sanctions [8,10]). For the purposes of the present work, we focus on definitions like the latter, which align with other recent empirical work on conventions (e.g., [11–13]). Importantly, norms do not necessarily concern multi-agent interactions, in the sense that the outcome is not contingent upon the actions of more than one individual – in other words they are not solutions to coordination problems. Recent work has also focused on similar distinctions to study and characterize non-human animal norms and conventions (e.g., [14,15]).

Defined in this way, conventions are characterized by three key properties [11]. First, they are efficient: once established in a population, each encounter with the same problem can be solved quickly, even if coordination partners vary (but only as long as these partners share the same convention). Second, conventions are arbitrary: the solution can take multiple forms, where one is not necessarily superior to another, and hence different populations may converge on different solutions. Third, conventions are self-sustaining: no individual benefits from deviating from the established convention on their own, and attempts to shift the convention at the population level can have disastrous consequences (the massive planning operation that accompanied Sweden’s overnight switch in 1967 from driving on the left to driving on the right represents a good example).

The emergence of conventions has been explored across several disciplines including linguistics, behavioral economics, game theory, computational social sciences, philosophy, and ethology, yielding a variety of insights into the mechanism of when and how conventions emerge [7,12,15–19]. Some approaches have focused on how external factors such as problem structure, solution space, or the network configuration of interacting individuals (e.g., [20–22]) impact the emergence of conventions. Other approaches have focused on exploring what higher-level cognitive processes scaffold the emergence of conventions at the population level (e.g., [7,17,23]), while yet others have explored how conventions scale up from small-scale interactions to the population (e.g., [24,25]). Recently, cognitively inspired computational models have aimed to understand the role of individual-level processes such as social learning (e.g., [26]) and reinforcement learning (e.g., [27,28]) in the emergence of conventions as well as how they scale up from pair-wise interactions to the population (e.g., [29]). While computational models with artificial agents have great potential for investigations at the level of large population and transmission over multiple generations, empirical human data is necessary to obtain better informed and sufficiently complex models so as not to fall into the trap of being too simple. To build better models, there are still gaps in our framework for understanding conventions, specifically the cognitive mechanisms at play at multiple levels, that require empirical data [16,30,31].

As outlined in recent reviews [8,31], conventions are theorized to emerge via multiple mechanisms operating at three different levels. At the individual level, basic cognitive abilities like learning and memory as well as more complex components of social cognition like imitation and reasoning about others are operational. At the group level (i.e., some subset of the population, with the smallest unit consisting of a dyad of two individuals), coordination may be based on joint goals. At the population level, demographic factors such as the rate of turnover in the population or the frequency of interactions with informed vs uninformed members of the population, or the population’s network structure, may affect the likelihood of the emergence of a population-wide convention. Wu and colleagues [31] propose that group-level processes are crucial to moving from individual-level processes to population-level solutions like conventions. They postulate that this occurs via two feedback loops, one between individual learning and group interactions (social learning facilitates coordination and vice versa) and the second between group interactions and large-scale societies (successful coordination facilitates shared knowledge and vice versa).

However, open questions remain about how group-level processes requiring coordination are facilitated when no societal-level shared knowledge (conventions) exist yet, potentially for a novel problem not yet encountered by the population. In these cases, we also do not know what/how individual-level processes are utilized at the dyadic level and how dyadic interactions scale up to population-level shared knowledge. Varying the conditions under which the same problem is presented to dyads allows manipulation of cognitive strategies that are available to the individuals as they complete a novel coordination task (e.g., [12,13]) and provides a way to gain insight into the underlying cognitive processes. For example, how a simpler mechanism like copying versus a more complex one involving setting expectations about one’s partner’s actions and intentions affect the emergence of a solution can be explored by manipulating visual access to the partner (copying is possible only when one can see the partner’s actions). Similarly, manipulating the amount of information the subjects have about the payoff allows us to modulate the desirability of achieving a joint goal for the pair. Solutions are likely to emerge quickly and efficiently when the subjects know they are required to coordinate, but how efficiently social coordination is achieved when these joint goals are not as concrete or transparent and have to be learned on the fly remains unclear.

To address these questions, we used a simple coordination paradigm involving a color-matching task. This paradigm was adapted from a recent study [11] showing the formation of simple conventions in a non-human primate, the Guinea baboon (Papio papio). Pairs of captive baboons were repeatedly presented with two colored squares on a computer screen, chosen randomly from a total of seven different colors. Subjects played in ever-changing pairs, and they were rewarded if both members chose the same color in any given trial. Over time, the baboons formed a convention consisting of a color preference hierarchy which allowed them to solve the task at above-chance levels. Importantly, this hierarchy was shared at the population level even though subjects only ever interacted in pairs. Furthermore, while subjects initially performed this task in a setting where they could see each other’s screens, they were also able to maintain their convention when an opaque partition was later introduced, and to form conventions when the experiment was repeated with a new set of stimuli and no visual access to the partner’s screen at any point. While Formaux and colleagues’ [11] study provides a valuable framework in which to study the emergence of conventions and was able to address Wu and colleagues’ [31] second feedback loop (between dyadic processes and transmission to the population level), open questions remain about the first feedback loop (between the individual and the dyad) as mechanisms at play at the individual level are difficult to disentangle (for example, the extent to which the subjects viewed the task as a coordination task rather than an individual task where they were sampling reward contingencies) and in turn how this contributes to the second feedback loop.

We therefore implemented the color-matching task with human dyads and under a variety of conditions to address how (i) varying how much information subjects had about the task structure (instructions vs no instructions), (ii) varying subjects’ visual access to their partner’s actions (transparent vs opaque), and (iii) introducing asymmetry in subjects’ prior experience with the task (experienced vs naïve) affected the emergence of conventions. We expected to see conventions emerge more often and faster when individuals had more information. We hypothesized that more conventions would emerge in the opaque condition compared to the transparent one, and that these conventions would be more stable since subjects would have to rely on shared color hierarchies to solve the task. We also hypothesized that pairs of subjects using conventions would have better overall performance on the task. By varying the order in which dyads were presented with the different conditions under (ii), and by examining how conventions that emerged in a given dyad were transmitted to naïve subjects under (iii), we could also characterize the maintenance of these conventions both within dyads as a function of visual access, and between dyads from different “generations”, respectively. For pairs starting in an opaque setting, we hypothesized that those who developed a convention would lose it when moved to a transparent setting, and those who did not develop a convention would remain unlikely to form one. For pairs starting in a transparent setting, we hypothesized that those who developed a convention would maintain it when moved to an opaque setting, while those who had not developed a convention would develop one. In dyads with an experienced subject, we expected conventions to be established more quickly than in dyads with two naïve subjects and that the experienced subjects would transmit their color hierarchies from their previous interaction to their naïve partners. In addition, we postulated that the different conditions would evoke varying levels of strategic behavior based on the cognitive complexity they present to the subject. Specifically, we hypothesized that the instructions conditions would prompt higher levels of strategic reasoning. We used subjects’ self-reported strategies to explore whether this was indeed the case. Our findings will help fill gaps in our theoretical knowledge of how different mechanisms may interact to give rise to solutions to novel coordination problems in dyads and how these solutions may transmit to and diffuse through larger populations.

2. Methods

2.2. Phase I

Eighty subjects completed a simple color-matching task adapted from Formaux and colleagues [11]. All subjects were initially naïve to the task and were assigned to pairs randomly, yielding a total of 40 pairs. Partners in a given pair were seated in front of 21.5-inch computer screens next to each other, at a distance of approx. 1 m. Each pair performed two sessions of 294 trials each, and, for the first session (Session 1), was randomly assigned to one of four conditions distinguished by (i) whether or not the subjects had visual access to each other’s screens (opaque vs transparent), and (ii) whether or not the pair was given specific information about what counted as a “correct” response in a trial (instruction vs no instruction). The four experimental conditions were constructed as different pairwise combinations of these settings, as described further below.

In the transparent (T) setting, subjects were able to see their partner’s screen, including the partner’s cursor and its movements, but a partition (76 cm x 51 cm black poster board held in place at 81 cm above the floor by a metal frame) was placed between them such that they could not see their partner to minimize any non-verbal communication between the subjects (Fig 1A). In the opaque (O) setting, the same partition was placed such that the subjects could not see their partner or their partner’s screen (Fig 1B, generated using AI (Google Gemini) and manually modified by the authors to ensure accuracy). In the instruction (I) setting, subjects were told in advance that they would score correctly on a trial (receiving 10 points) if they and their partner chose the same color; those in the no-instruction (NI) setting were only told that whether or not a trial was scored as correct depended on both their and their partner’s choice. The four conditions tested in Session 1 were therefore I-T, I-O, NI-T, and NI-O with 10 pairs assigned to each condition (see S1 Table for a distribution of age and sex of our subjects across the conditions). For Session 2, performed immediately after Session 1, each pair’s visual access was reversed but no further instructions were provided. This meant that I-T and NI-T pairs became I-O and NI-O pairs, respectively, while I-O and NI-O pairs became I-T and NI-T, respectively. Subjects were instructed not to communicate with each other in any way throughout both sessions or during any breaks, and to try to maximize their cumulative score.

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Fig 1. Task set-up and trial progression.

Subjects and apparatus in the (A) Transparent condition, where subjects can see each other’s screen but not each other, and (B) Opaque condition, where subjects cannot see each other’s screen or each other (images were generated by AI (Google Gemini) and modified). (C) and (D) show trial progression on both subject’s screens for a correct and an incorrect trial, respectively. In (C), where both subjects choose the same color, a results screen showing a reward of 10 points for that trial (“round”) appears. In (D), where the subjects choose different colors, they see a brief red flash on the screen followed by results screen showing 0 points obtained for the trial. In both cases, total score is tracked and shown on the results screen. If one player chooses first, a waiting screen is displayed until the other player makes a choice.

https://doi.org/10.1371/journal.pone.0341532.g001

The task used seven different colors (identical to those used by Formaux and colleagues [11]), offering a total of 21 different pairwise combinations. In each session, these sets of 21 combinations were presented repeatedly over 14 consecutive blocks (where the order of pairings within each 21-trial block was randomized) yielding a total of 294 trials per session. This number of trials was determined to be adequate to observe the emergence of conventions (arbitrary rankings of colors that determined choices in any given color pairing) through pilot studies. Each session lasted ~20–30 minutes. Subjects were prompted to take a break every 98 trials, resulting in two breaks per session.

At the start of Session 1 instructions were presented on the screen and the task began once both subjects indicated that they were ready by clicking on a start button (see online repository for exact instructions). In each trial, two colored squares (200x200px) were presented against a black background on the left and right side of the subjects’ screens. The left-right locations of the colors were randomized such that in ~50% of the trials the two colors appeared in the same location for the two subjects and in the remaining ~50% of the trials they appeared in the opposite locations) – this was to ensure location could not be used as a basis for matching. The subjects had to make a choice by mouse-clicking on one of the squares. Either subject could respond first and whoever responded first was shown a screen indicating that the other subject had not yet responded. Once both subjects had responded, an identical feedback screen was displayed on both screens informing subjects either (i) that they were correct and would be rewarded with 10 points or (ii) that they were incorrect and would receive 0 points (see Fig 1C and 1D, respectively). Their total score up to that point was also displayed. The next trial then commenced once both subjects indicated their readiness by clicking the “Next” button.

Once a pair had completed Session 1, they were allowed to take a 5-min break in which they were not allowed to communicate with each other, and once both subjects were ready the second session began. The same instructions page presented at the beginning of Session 1 was shown as a reminder with no new information, and the same set of colors from Session 1 were used. Crucially, the partition was moved during the break so as to switch between the opaque and transparent settings.

At the end of each session, subjects were asked to report the strategies they used to solve the task in a free-response questionnaire. For both sessions, across all four conditions, the partition was used to cover the partner’s screen from view while typing the response to ensure subjects did not see their partner’s description of their strategy.

2.4. Analysis

2.4.1. Phase I session 1.

Overall performance. For each pair in each session, we recorded the total number of correct responses scored, as well as the pair’s mean response times across all trials. Response times in each trial were measured from the time the colored squares appeared on the screen until a subject clicked on the screen (for individual-level reaction time) and once both subjects had chosen a color (for pair-level reaction time). We also classified each pair as having either developed or not developed a convention during a given session based on whether or not the two subjects of the pair showed evidence of matching color hierarchies in their responses (see “Color hierarchies” and “Emergence of conventions” sections below), and tested whether the proportion of pairs with conventions differed across conditions using a Fisher’s exact test (fisher.test() from the R package “stats”). Accuracies and pair-level mean reaction times were compared between convention-forming and non-convention-forming pairs using two-tailed t-tests. For subjects in pairs with a convention, individual reaction times across trials before the emergence of the convention and across trials after the emergence of the convention were compared while accounting for general decrease in reaction time as trials progressed (learning effect). This was achieved using a linear mixed effects model with log of the reaction time (after removing outliers using ± 2.5 SD) as the dependent variable, and trial number, condition, and whether the trial was before a convention emerged (0) or after (1) were used as independent variables. A random effect of pair was added to account for the non-independent nature of reaction times of subjects from the same pair. If the interaction between the two independent variables was not statistically significant then the regression was rerun without the interaction term. Assumptions about the data required for running a linear regression were confirmed through visual inspection of the distribution of the dependent variable. The lme4 and lmerTest packages in R (R version 3.4.1, [33]) were used for the linear mixed effects model and for obtaining p-values using Satterthwaite’s degrees of freedom method, respectively.

Color hierarchies. For each individual subject, we analyzed their pattern of responses by tracing the evolution of their preferences for each of the seven colors over the course of both sessions. In the opaque conditions (I-O and NI-O), there was only one way to solve the task with accuracies above chance level: the two subjects needed to establish a shared hierarchy of color preferences. This would ensure that when presented with any combination of two colors, both subjects would be able to choose the same one. In the transparent conditions (I-T and NI-T), this strategy was one of two possible solutions; the other involved the trial-by-trial use of social information (one player choosing a color and the other player copying it). This second strategy did not require a consistent color hierarchy.

To measure the emergence of color hierarchies, we calculated and tracked Elo-ratings for each color trial-by-trial, separately for each subject, following Formaux and colleagues [11]. Elo-ratings were first developed to rank chess players [34] but more recently have also been used to construct social dominance hierarchies in behavioral ecology (e.g., [35]). The Elo-rating method continuously updates interactants’ ratings based on the outcome of each observed interaction between them (e.g., win/lose). We applied the Elo-ratings R package [35] to the seven colors, separately for each subject, treating each color as an “individual”. At the start of the session, all the colors were assigned a default Elo-rating of 1000. Then, at the end of each trial the color from the current pairing that was chosen by the subject (i.e., the “winner” of the interaction between the two colors) received a boost to its Elo-rating while the Elo-rating of the color not chosen by the subject (the “loser”) decreased by the same amount. This continuous updating across the trials allowed us to visualize the evolution of color preferences for each individual subject over the course of both sessions. Fig 2A shows an example of a subject that developed a clear hierarchy of color preferences, Fig 2B shows a subject with a partial hierarchy where there was a preference for darker over lighter colors but the relative rankings of some of the colors fluctuated, and Fig 2C shows a subject who did not seem to have developed a hierarchy of color preferences.

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Fig 2. Examples of the evolution of Elo-ratings for the seven colors used in the experiment (three different subjects; Session 1 only).

(A) shows a subject with a clearly discernible color hierarchy; (B) shows a subject with a partial hierarchy (only some colors’ ranks in the hierarchy are well separated); and (C) shows a subject who did not develop a color hierarchy.

https://doi.org/10.1371/journal.pone.0341532.g002

The task allows the pairs to converge on any hierarchy of the seven colors (out of a total of 7! = 5040 different possible hierarchies). To test whether there was any universality in preferences, the average rank of each color across the hierarchies used in pairs with conventions was calculated and Kendall’s W was used to measure agreement of color order across the pairs.

Emergence of conventions. Qualitatively, we defined a convention as a situation in which the color hierarchies of the two subjects in a pair matched. To establish whether and when this point was reached in a given session, we defined three different measures of accuracy: individual accuracy, pair accuracy, and combined accuracy. Individual accuracy was a measure of how consistent an individual subject’s choices were with their own hierarchy of color preferences developed up to that point. It was encoded as a binary variable at each trial: 1 if the subject chose the color with the higher current Elo-rating and 0 if the subject chose the other. Pair accuracy, calculated for the pair at each trial, served as a measure of whether the choices of the two subjects in the pair matched (and hence whether they had solved the trial correctly). It was also encoded as a binary variable: 1 if both subjects chose the same color and 0 if they chose different colors. Combined accuracy combined both of these measures using a logical AND operator, i.e., combined accuracy was 1 for a trial only if both subjects had an individual accuracy of 1 and the pair accuracy was 1. This ensured that a combined accuracy of 1 could only be achieved if a color hierarchy emerged that was shared by the two subjects.

At the trial level, a combined accuracy of 1 still did not indicate a “convention” since it was possible to obtain this by chance. We used a rolling window (of size 21 trials) to track mean combined accuracy and defined a criterion above which it had to be maintained in order for the pair to qualify as having a convention. We chose a threshold of 80% so as to not penalize the pair for momentary lapses in attention and memory as well as minor confusions between color rankings. The pair had to maintain performance above this threshold for at least 21 consecutive overlapping windows (i.e., a total of 42 trials, which ensured that all unique pairings of colors were presented at least once). The first trial of these 21 windows was defined as the point of emergence of a convention for the pair. S1 Fig shows complete data for two example pairs, with panels C and G demonstrating combined accuracy as a function of trial number for a pair that reached a convention at trial 133 and a pair that did not develop a convention, respectively.

For the pairs where a convention was observed to emerge, we tested if there was a significant effect of condition on the time taken for the convention to emerge using a multiple linear regression model with instruction type (I vs. NI) and visual access type (O vs. T) as two independent variables and trials-to-convention as the dependent variable.

Assumptions about the data required for running a multiple linear regression including normal distribution of residuals and homoscedasticity were confirmed through visual inspection of the histogram of residuals, while the lack of multicollinearity of the independent variables was ensured by their orthogonal nature. If the interaction between the two independent variables was not statistically significant then the regression was rerun without the interaction term. As a follow-up, if the linear model was significant, two-tailed independent t-tests were performed to determine the direction of the effects observed (lm() and t.test() from R package “stats” were used here and in following regressions and follow-up t-tests). Similar methods were used for all following linear models. All tests for statistical significance were performed with alpha set to 0.05.

Stability of conventions. The metric pinpointing the emergence of a convention ensures that both subjects share a color hierarchy (to a certain degree) and are able to successfully complete the task (choose the same color) for a minimum number of consecutive trials. However, this metric does not consider the stability of the convention. For example, a pair of subjects could successfully maintain their convention for the required number of trials but then experience a drop in performance if one or both subjects deviate from the established color hierarchy. Therefore, the strength or stability of the convention also needs to be evaluated. We used a measure of stability based on “crossovers” in Elo-ratings, i.e., the frequency of changes in color rankings for each individual once a convention emerges. We used a version of the stability calculations, from the Elo-ratings package [35], that did not implement weightings (weight is relevant for animal dominance hierarchies where switches in rank between two high-ranking individuals are considered to disrupt stability more than switches between two low-ranking individuals). The formula for calculating color hierarchy stability, S, adapted to our task is shown in Equation 1, where n is the trial where a convention first emerged for a pair and X_ij is the Elo-ranking of color j in trial i. Values for S range between 0 and 1, with 0 being the least stable and 1 indicating no changes in rank observed. Stability was calculated for 100 trials after a convention was reached to ensure both that sufficient number of trials and the same number of trials were included in the calculation across all the pairs. Pairs that did not have 100 trials remaining after they established a convention were excluded from this analysis (leading to the exclusion of two pairs, see Results); however, to ensure that our choice of 100 trials did not influence the results, we reanalyzed the data using all available post-convention trials for all pairs. Stability was calculated for each subject and averaged across the two subjects in a pair to obtain a mean stability for the pair.

(1)

We tested whether the stability of the conventions varied as a function of condition using a multiple linear regression model with instruction type (I vs. NI) and visual access type (O vs. T) as two independent variables and the arcsine-transformed mean stability of the pair as the dependent variable.

Self-reported strategies. In strategic games, it is hypothesized that players assign levels of strategic behavior to their partners, employing varying levels of cognitive complexity [36]. We analyzed the subjects’ self-reported strategies by assigning them to one of three levels. Level 0 corresponded to subjects who did not indicate that they took their partner’s actions into account. Level 1 players assumed their partner was playing at level 0 and played accordingly. Level 2 players assumed their partner was at least level 1, i.e., that their partner also had a strategy that took their actions into account (S2 Table shows hypothetical examples used by coders as guidelines and examples of subject-reported strategies). The strategies were rated by two coders, one who was aware of the goals of the study and one who was not. There was substantial agreement between the two coders (Cohen’s Kappa, κ = 0.74). Ratings where there was mismatch (12 subjects) were assigned a final rating via discussion between the two coders.

For each pair, we calculated the minimum level of strategy used by the two subjects as well as the maximum level. A multiple linear regression model with instruction type (I vs. NI) and visual access type (O vs. T) as two independent variables and strategy (either minimum or maximum strategy) as the dependent variable was used to test whether the different conditions evoked the need for less or more complex cognitive strategies. These analyses were conducted only with Phase I Session 1 data for 39 out of the 40 pairs; one pair’s strategy was only partially saved due to a technical error and was thus not used for this analysis. For pairs with a convention, a multiple linear regression model with instruction type (I vs. NI) and visual access type (O vs. T) as well as minimum or maximum strategy as independent variables and trials-to-convention as the dependent variable was used to test if level of strategic behavior had an effect on how quickly conventions emerged. These models were compared to the model described in the “Emergence of conventions” section as a null model (without strategies) for 18 out of the 19 pairs with conventions (as one pair’s data was lost due to a technical error).

2.4.2. Phase I session 2.

Maintenance of conventions across conditions. Data from Session 2 were used to explore whether conventions that formed in Session 1 were maintained across a change in visual access. The same metrics as for Session 1 were calculated, with one key difference: the Elo-ratings of the colors at the beginning of Session 2 were set to the final Elo-ratings at the end of Session 1 to ensure a fair assessment of convention emergence and/or maintenance (starting at 1000 again would have invalidated the hierarchy/knowledge that the subjects had built up in Session 1).

Pairs in T and O conditions in Session 1 (I and NI were collapsed since by the end of Session 2, every pair had had a chance to play in the T setting and thus could be assumed to have understood the task reward/payoff structure), were split into “Convention” and “No Convention” based on whether they had reached a convention in Session 1. Within each of these groups the pairs were further divided into “Convention” and “No Convention” based on their performance in Session 2. This allowed us to evaluate which conditions were conducive to the formation, maintenance, or abandonment of a convention with a change in visual access.

2.4.3. Phase II.

Overall performance. Metrics for overall performance, and for the emergence and stability of conventions, were calculated for the Phase II pairs in the same manner as in Phase I Session 1, and compared to pairs in the instruction and opaque condition (I-O) of Phase I. We tested whether the proportion of pairs with conventions differed between Phases I and II using a Fisher’s exact test. A two-tailed t-test was used to determine whether the time taken for a convention to emerge and the stability of the conventions differed between I-O pairs from Phase I and Phase II pairs.

Transmission of conventions. For the pairs that had a convention emerge in Phase II, Spearman rank correlations were calculated among all possible pairings of (i) the experienced subject’s color hierarchy at the end of Phase I, (ii) the color hierarchy they recalled at the beginning of Phase II, (iii) the color hierarchy developed by the experienced subject at the end of Phase II, and (iv) the color hierarchy developed by the naïve subject at the end of Phase II. These correlations were designed to test the extent to which conventions were transmitted across the phases and within Phase II. In particular, since the gap between Phase I and Phase II was rather long (ranging from 42 to 126 days, Mean = 71.5, SD = 16.77), the experienced subject’s recalled hierarchy was of primary interest for determining whether their specific color rankings were transmitted to the naïve subject. For each correlation of interest, the values were averaged across all the pairs to test for significance at the group level.

3. Results

3.1. Phase I session 1

Overall performance. The emergence of a color-hierarchy convention was determined for pairs across conditions based on sustained combined accuracy (where both subjects in the pair chose the same color and that color choice matched the color hierarchy each subject had built up until that point). We hypothesized that the instructions condition, where subjects had more information about the task’s payoff structure, would see more conventions emerge across the pairs. We also hypothesized that the opaque condition would see more conventions emerge since subjects had to rely on shared color hierarchies to solve the task, while those in transparent conditions had the option to watch and copy their partner. We expected pairs using a convention to solve the task would have better overall performance. We found that conventions emerged in all experimental conditions: 6 out of 10 pairs established color-hierarchy conventions in I-O, as did 3 out of 10 in I-T, 6 out of 10 in NI-O, and 4 out of 10 in NI-T. Thus, contrary to our expectations, having more information about the task did not translate into more conventions: instructions resulted in a similar number of conventions (9/20) as no instructions (10/20), and while opaque conditions contained more pairs with conventions (12/20) than transparent conditions (7/20), a Fisher’s exact test showed that the difference among conditions was not significant (two-tailed, p = 0.538). Overall accuracy (percentage correct) in the task was significantly higher in pairs that used a convention (mean ± SD = 89.92 ± 8.81, n = 19) than in those that did not (mean ± SD = 76.43 ± 23.74, n = 21; t(25.9) = 2.36, p = 0.026, Fig 3A). Mean reaction time for pairs with a convention (mean ± SD = 1.71 ± 0.24 s, n = 19) did not differ significantly from those without a convention (mean ± SD = 1.34 ± 0.50 s, n = 21; t(18) = 2.03, p = 0.057). However, for pairs with a convention, even after controlling for a general decrease in reaction time with task progression, there was a decrease in reaction times after a convention emerged in conditions NI-O (β = −0.29, p < .001), I-T (β = −0.13, p = .032), and NI-T (β = −0.15, p = .005), but not in I-O (β = 0.035, p = .450; see raw data for all conditions in Fig 3B).

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Fig 3. Phase I Results: Emergence, Stability and Maintenance of Conventions.

(A) Overall scores for pairs without conventions (hollow purple dots) and with conventions (solid orange dots). (B) Reaction time for subjects in pairs with a convention across trials before (hollow purple dots) and after (solid orange dots) a convention emerged, excluding outliers. (C) Trials taken to reach a convention in pairs that had a convention (solid orange dots). Hollow purple dots indicate pairs that did not converge on a convention and were not included in the calculation of the means for each condition. (D) Mean stability of the conventions that emerged across the four conditions. For all box plots, upper and lower bounds of box represent upper and lower quartiles, respectively, center of the box represents the median, and the whiskers extend to maximum and minimum (outliers are calculated ± 1.5 * inter-quartile range past the upper and lower quartiles). (E) Number of pairs that maintained, lost or newly developed a convention as they transitioned from transparent session 1 to opaque session 2 (left) or opaque session 1 to transparent session 2 (right).

https://doi.org/10.1371/journal.pone.0341532.g003

Color hierarchies. We observed a variety of different color hierarchies across the 19 pairs that had developed a convention. Although some colors seemed to be preferred over others at the population level – for example, colors from the blue/purple end of the spectrum as well as pink were preferred over yellow, orange, and brown – we found weak agreement of color order across the pairs with conventions (Kendall’s W = 0.054, p = 0.056; see S2 Fig).

Emergence of conventions. The point of emergence of a convention for each pair was determined as the trial where they achieved above 80% combined accuracy. We hypothesized that pairs with more information (instructions) would reach a convention sooner. The overall regression was statistically significant (R² = 0.33, F(2, 16) = 5.38, p = 0.016), suggesting that the time taken for a convention to emerge varied between conditions. Visual access did not significantly predict time taken to reach a convention (β = −23.58, p = 0.392); however, instructions did (β = −75.26, p = 0.013). Of the pairs that reached a convention across both types of visual access (opaque and transparent), those with instructions (pairs that were explicitly told that choosing the same color would yield a reward) took longer (mean ± SD = 151.44 ± 65.28, n = 9) to reach a convention than those with no instructions (mean ± SD = 69.90 ± 45.73, n = 10; t(17) = 3.18, p = 0.005, Fig 3C).

Stability of conventions. Stability of the conventions that emerged was calculated as a function of cross-overs in the rankings of colors in each individual subjects’ hierarchies, across 100 trials post-emergence. We hypothesized that stability of conventions that emerged in opaque conditions would be higher compared to transparent conditions. Stability was only calculated for four of the six pairs with a convention in I-O since in two of the pairs the convention emerged late in the session, leaving fewer than 100 (23 and 87) trials to analyze. For all other conditions, all pairs with conventions were used in the calculation of stability. The overall regression was statistically significant (R² = 0.62, F(2, 14) = 13.87, p < 0.001), suggesting that the stability of conventions varied between conditions. Instructions did not significantly predict the stability of a convention (β = −0.005, p = 0.795), but visual access did (β = −0.088, p < 0.001). Of the pairs that had a convention across both types of instruction conditions, those with no visual access (opaque, mean ± SD = 0.993 ± 0.003, n = 8) had more stable conventions than those with visual access (transparent, mean ± SD = 0.969 ± 0.015, n = 9; t(15) = 4.47, p < 0.001, Fig 3D). To ensure that our choice of 100 trials did not influence these results, stability was also calculated across all post-emergence trials for all pairs with a convention (S4A Fig); the results remained unchanged.

Self-reported strategies. Strategies reported by the subjects were coded for level of strategic behavior, and both minimum and maximum levels reported in a pair were used to test whether condition influenced the strategy used by the subjects. We hypothesized that instructions would prompt the engagement of higher levels of strategic reasoning. The overall regression was statistically significant for minimum strategy used by the pair (R² = 0.13, F(2, 36) = 3.88, p = 0.030), suggesting that condition had an effect on the minimum level of strategic behavior used by pairs. Visual access significantly predicted the minimum strategy used (β = 0.42, p = 0.01); however, instructions did not (β = 0.08, p = 0.630). Pairs in the transparent conditions had a higher minimum strategy (mean ± SD = 0.90 ± 0.45, n = 20) than those in the opaque conditions (mean ± SD = 0.47 ± 0.51, n = 19; t(35.73) = 2.76, p = 0.009). The overall regression was not statistically significant for maximum strategy used (R² = −0.02, F(2, 36) = 0.64, p = 0.534), suggesting that condition did not affect the maximum level of strategic behavior elicited.

To test whether the strategy used influenced how quickly a convention emerged, the regression model from the “Emergence of conventions” section was rerun for the pairs with both conventions and strategy data available (18 pairs, as opposed to 19 pairs with conventions previously), yielding similar significant results as above (R² = 0.31, F(2, 15) = 4.90, p = 0.023). Adding minimum strategy as an independent variable did not improve the model (R² = 0.28, F(3, 14) = 3.18, p = 0.057) and neither did adding maximum strategy as an independent variable (R² = 0.28, F(3, 14) = 3.18, p = 0.057).

3.3. Phase II

Overall performance. Subjects that developed a convention in Phase I were paired with naïve subjects who had not completed this task before. The same analysis outlined for Phase I for calculating the emergence and stability of conventions were performed for these pairs and compared to pairs from the I-O condition in Phase I. We hypothesized that the presence of an experienced player would allow pairs to establish conventions more readily and more quickly than pairs of naïve subjects. Of 21 such pairs tested in Phase II, 13 developed a convention. This proportion (13/21) did not significantly differ from that observed in Phase I Session 1 pairs (I-O condition: 6/10, p = 1.000). However, Phase II pairs reached a convention significantly faster than pairs in Phase I (I-O) (Phase II: mean ± SD = 121.46 ± 38.83 trials; Phase I: mean ± SD = 174.5 ± 59.19 trials; t(17) = 2.37, p = 0.030; see Fig. 4A). There was no significant difference between the stability of conventions in Phase II (mean ± SD = 0.993 ± 0.004, n = 13) and pairs in Phase I Session 1 I-O that had a convention (mean ± SD = 0.995 ± 0.002, n = 4; t(15) = 0.65, p = 0.526, Fig 4B). To ensure the choice of 100 trials did not influence these results, stability was also calculated for all remaining post-convention trials of the session for all pairs with a convention (S4B Fig).

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Fig 4. Phase II Results: Transmission of Conventions.

(A) Trials taken to reach a convention in the pairs that had a convention (solid orange dots) in Phase I (Session 1 I-O condition; 6/10) compared with those in Phase II (13/21). Hollow purple dots indicate pairs that did not converge on a convention and were not included in the calculation of the means for each condition. (B) Mean stability of the conventions that emerged in Phase II compared with mean stability of conventions in Phase I (Session 1 I-O condition). In A and B, upper and lower bounds of boxes represent upper and lower quartiles, respectively, center of the box represents the median, and the whiskers extend to maximum and minimum (outliers are calculated ± 1.5 * inter-quartile range past the upper and lower quartiles). (C) Mean correlations across pairs in Phase II that had a convention among (i) Experienced – Phase I: the experienced subject’s color hierarchy at the end of Phase I, (ii) Experienced – Recall: the color hierarchy experienced subjects recalled at the beginning of Phase II, (iii) Experienced – Phase II: the color hierarchy developed by the experienced subject at the end of Phase II, and (iv) Naïve – Phase II: the color hierarchy developed by the naïve subject at the end of Phase II.

https://doi.org/10.1371/journal.pone.0341532.g004

Transmission of conventions. To test whether the experienced subjects transmitted their memorized conventions from Phase I, correlations across the hierarchies in the two phases were calculated. We hypothesized that experienced subjects would transmit color hierarchies from their previous pair – or, specifically, the hierarchy they recalled from Phase I at the start of Phase II. Fig 4C summarizes all correlations among experienced subjects’ Phase I color hierarchies, their recalled hierarchies, their Phase II hierarchies, and the hierarchy developed by the naïve subject in Phase II. Only 2 out of the 21 experienced subjects had significant recall correlations (meaning they were able to remember their previous hierarchies from the end of Phase I; ρ(7) = 0.89, p = 0.007 and ρ(7) = 0.86, p = 0.013). Neither these two subjects, nor the set of experienced subjects as a whole, transmitted their Phase I hierarchies to the naïve subjects: we found no significant mean Spearman rank correlations between the experienced subjects’ hierarchies at the end of Phase I (or their recalled hierarchies) and their naïve partners’ hierarchies at the end of Phase II. Only one pair had a significant correlation between the experienced subject’s recalled hierarchy and the transmitted hierarchy, but, interestingly, this was a negative correlation (ρ(7) = − 0.89, p = 0.007).

4. Discussion

The use of conventions – arbitrary, self-sustaining practices that emerge in a population and facilitate efficient solving of a specific coordination problem – is a ubiquitous aspect of human behavior and communication [7,8]. Nevertheless, many open questions remain surrounding the process through which conventions are established and maintained, the level of cognitive sophistication required, as well as the group-level processes that facilitate their emergence. Our study demonstrates the emergence of simple conventions in experimental human pairs for solving a novel coordination problem presented across a number of conditions, even in the absence of communication. Specifically, we examined how subjects’ knowledge of the structure of the problem, their access to their partner’s actions, and their prior experience with solving the task affected whether and how quickly the conventional solution was found by a given pair. We further analyzed the stability of the conventions formed as a function of these conditions as well as the transmission of conventions from knowledgeable to naïve individuals (simulating how established conventions may be conserved under demographic turnover in a hypothetical population). Strategies reported by the subjects at the end of their session were used to both quantitatively and qualitatively assess the cognitive processes that may have been recruited for the successful completion of the task, as well as other conventions that may have emerged (see below).

Crucially, all three key features of conventions (efficient, arbitrary, self-sustaining) were evident in our data. First, we were able to confirm that pairs with a convention outperformed those without, achieving higher overall scores, and demonstrated lower reaction times per trial once a convention emerged in three out of four conditions. Second, we observed a number of different color hierarchies, with no statistically significant agreement across pairs in the ranking of the colors (although some colors did appear to be highly ranked by more pairs than others, possibly due to salient features such as brightness), demonstrating the arbitrariness of the solutions that emerged. Third, conventions that emerged exhibited high levels of stability, especially in the opaque conditions. Although three pairs that developed a convention in their first session lost it following a change in visual access to the partner’s actions (second session), the majority (16 out of 19) maintained theirs even across this shift – exhibiting stability across changes in context (which in this case was visual access to partner’s screen). Indeed, the three pairs that “lost” their convention were later confirmed to have relied on a copying strategy where only one subject had internalized a color hierarchy. Thus, all “true” color-hierarchy conventions were self-sustaining across changes in visual access.

Our Phase I Session 1 results also indicate, contrary to our expectations, that having more information about the structure of the problem does not necessarily increase the speed with which conventions are first established. In fact, we observed the opposite of such an effect: in the two conditions where our subjects had explicit instructions that choosing the same color would yield a reward (I-O and I-T), i.e., they knew what counted as a case of successful coordination from the start, conventions took longer to emerge. We hypothesize that having more information about the task structure could have resulted in the subjects paying more attention to their partner’s actions (when visible), as well as potentially building mental models of their partner’s strategy (whether or not the partner’s actions were visible). This in turn may have led to a form of heightened reactivity and over-correction, resulting in oscillations rather than convergence between partners. A similar phenomenon was observed by Roberts and Goldstone [37] in a collective task where groups attempted to reach a target sum through individual contributions: the authors found that when every member reacted to the feedback simultaneously, the group’s total oscillated around the target, while when most members kept their responses consistent, allowing a few individuals to make the necessary adjustments, the group was more successful. A parallel in our task would be the emergence of a leader-follower dynamic, where one player maintains a consistent color hierarchy while the other adjusts their responses, rather than both individuals simultaneously trying to signal a convention and model their partner’s hierarchy leading to unstable oscillations (see below for a discussion of the possible emergence of such a leader-follower strategy in the transparent condition). This and other asymmetries between players in how they model and respond to their partner likely affect the likelihood with which we observe relatively rapid convergence on a convention versus extended oscillatory behavior.

In contrast, a simpler reward-contingency-based approach, in which subjects repeatedly sample the environment and build up expectations about the relative payoff likelihoods of the different colors, without forming any beliefs about their partner, could have yielded faster convergence on a conventional solution in the conditions with no instructions (NI-O and NI-T). Indeed, such a strategy likely explains baboon subjects’ convergence on a hierarchy of stimuli in Formaux and colleagues’ [11] study, most saliently in the condition where monkeys had no visual access to their partner’s choices at any point during learning (experiment 2.2). This hypothesis is also in line with findings in the game theory literature where reinforcement learning leads to faster convergence to a solution compared to more complex strategies that attempt to predict the partner’s behavior (e.g., [38–40]). However, our analysis of the levels of strategic reasoning employed by subjects – as reflected in their self-reported strategies – did not support this hypothesis, in that we found that condition (I vs NI) did not significantly predict subjects’ level of strategic reasoning. Nonetheless, we recommend caution in the interpretation of these results since subjects’ strategies were obtained from a free-response questionnaire where different subjects responded with varying levels of detail. To better tease apart underlying mechanisms, a more specific post-session questionnaire would be required, carefully crafted so as not to bias subjects into reporting, for example, more complex strategies (via retrospection) than the one that they actually employed during the task. In addition, if our hypothesis that simple tracking of reward contingencies would yield faster and more stable convergence on a color hierarchy convention is correct, we would expect pairs in a version of this task where they are unaware of their partner (i.e., do not even know it is a coordination task) to outperform those in both the Instruction and No Instruction conditions.

In contrast with our speed-of-emergence comparisons, the stability of conventions did not vary as a function of the information provided to subjects at the beginning of the experiment. It did, however, vary with visual access: conventions in opaque conditions (I-O and NI-O) were more stable than those in transparent conditions (I-T and NI-T). This was as expected: in opaque conditions a color-hierarchy convention was the only way to solve the task, whereas in transparent conditions subjects could instead also use social information trial-by-trial (i.e., check the partner’s screen for their choice and copy it), likely leading to the less stable color hierarchies we observed. In addition, visual access also appeared to influence the level of strategic reasoning elicited in the subjects: the minimum strategic level employed by pairs was higher in the transparent conditions than in the opaque conditions. This was surprising given the availability of the copying solution in the transparent conditions but may suggest that visual access to a partner’s actions prompted the engagement of higher-level processing of social information. If accompanied by higher responsivity to the partner’s actions (including to any choices made in error, i.e., not matching a currently established color hierarchy), then such higher-level reasoning about the partner may, in turn, have been another factor responsible for the increased changeability (lower stability) of color hierarchies in the transparent conditions.

Indeed, the availability of a copying strategy under the transparent conditions represents an important caveat. While a shared hierarchy of colors is one possible convention that enables fast and consistent solving of the task, division of labor or turn-taking are also kinds of conventions that can serve as solutions to coordination problems (e.g., [13]). For example, in our task, an alternative convention in the transparent conditions would see one of the subjects emerging as the leader or “proposer”, i.e., the one who consistently chooses one of the two options first, and the other becoming the follower or “responder”, who then chooses the same color as the proposer (this was in fact an integral aspect of the design in Formaux and colleagues’ [11] study with baboons, although there the roles were randomly assigned for each session). This strategy is efficient since the consistency in roles removes the uncertainty about who should choose first on each trial and thus neither partner is delayed in attending to their half of the task (choose color for the proposer, and copy partner for the responder). As such, this alternative strategy also carries the hallmarks of a convention: not only is it efficient, but it is also arbitrary in that either player could assume either role, and it is self-sustaining in that an attempt by one subject to reverse the roles would interfere with the efficient solving of the task (at least temporarily). However, it is unclear how such a convention would scale up to the population level: coordination would emerge quickly whenever a proposer and a responder happen to meet, but two proposers or two responders would experience difficulty. A color-hierarchy-based convention, as long as it is shared by the population, would ensure efficient solving between any two randomly chosen individuals from the population (the nationally mandated driving conventions referenced in the Introduction represent a clear example).

We were not able to determine from the trial-by-trial response data which pairs adopted a proposer-responder convention (with or without also establishing a shared or unshared, i.e., proposer-only, color hierarchy): in theory, reaction times could reveal which player chose first, but in practice we observed that proposers tended to move their cursor over the color they were about to choose, waited for the responder to also move their cursor over the same color, and then both subjects clicked simultaneously, leading to near-identical reaction times. Nonetheless, other lines of evidence do suggest the emergence of such a convention in some pairs. First, strategies reported by subjects in transparent conditions (across both I and NI) included explicit mentions of a given subject “following” the choices of their partner consistently. Second, in some pairs we observed that one subject had a very strong side bias (for example, would always click right) while the partner had roughly a 50% chance of clicking either left or right, indicating that the former likely acted as a proposer who did not use a color hierarchy while the latter acted as a responder who simply copied the choices of the proposer. Finally, three pairs exhibited a curious pattern where they appeared to have generated a color-hierarchy convention in their transparent Session 1 (where a convention was not essential for solving the task) but immediately lost it in the following opaque Session 2 (where it was necessary). It is likely that instead of these pairs having established a convention in the form of an arbitrary shared hierarchy of colors, one subject was using a color hierarchy in the transparent session while the other was simply copying without being explicitly aware of the hierarchy. Interestingly, we found that pairs with “true” color conventions were faster at the task at the trial level than these pairs. This suggests that within the framework of our task, the color-hierarchy convention was not only more robust to changes in context (presence vs absence of visual access) than the proposer-responder convention, but also overall more efficient in a context where both types of convention were available to subjects.

These varied outcomes in how pairs approached our task allow us to speculate about the role of specific cognitive mechanisms that support the different kinds of conventions available to subjects. We argue that the establishment of a shared color hierarchy between players required, at minimum, the ability to track reward contingencies obtained through environmental sampling over time (where these reward contingencies are, unbeknownst to one player, being modified in real time by the other player). In fact, this ability may be a necessary and sufficient condition enabling the gradual emergence of a shared color hierarchy, extending even to cases where subjects are not aware of the existence or role of a partner. In contrast, a strategy involving copying of the partner may require additional social cognitive skills: at minimum it relies on the capacity for social information use and learning to map the appropriate response to the partner’s observed choice, but can also be supported by more complex forms of ‘cognitive imitation’ [41] where the subject copies a cognitive rule that it infers the partner is using. Copying skills are prominent in humans [42,43], and while they are likely also present among non-human primates, monkey and ape subjects typically require extensive training before they are able to use the choice behavior of another individual as the basis for their own choice [41,44]. While baboon pairs in Formaux and colleagues’ [11] study could not spontaneously develop a proposer-responder convention given that the experimental design automatically assigned one baboon as the proposer and the other as the responder on every trial, they were observed to watch their partner before responding only when the two colors had similar Elo-scores (and hence the trial was “difficult”). In contrast, over a third of our pairs in transparent conditions developed a proposer-responder convention reliant on copying.

Moreover, our human pairs also leveraged other cognitive abilities: for example, despite our instructions specifying that subjects were not allowed to communicate with each other, behaviors such as hovering over the chosen stimulus until the other player’s cursor arrived at the same color arguably circumvented this constraint. In addition, subjects’ self-reported strategies also revealed a tendency to attend at least to the choices of the other player and, in some cases, to take this further by speculating about the other player’s strategy and future behavior based on their prior choices. Such modelling of the other player’s mind would appear to recruit advanced socio-cognitive skills (such as theory of mind) potentially unique to humans. Interestingly, we suspect that one of the reasons for the delayed emergence of color-hierarchy conventions in our Instruction conditions was that knowing more about how the partner’s choice influenced trial outcomes prompted the increased engagement of high-level social cognition. Specifically, this engagement could have led to oscillations in players’ choices as each player attempted to “catch up” with their partner (e.g., on an “incorrect” trial, both players may infer that the other player selected the other color leading both to adjust their own choice, with the same incorrect outcome on the next trial and hence both shifting their choice again, and so on). Hence, somewhat counterintuitively and potentially as an artefact of our experimental design prohibiting overt communication, we found that simpler cognitive strategies likely enhanced the speed with which conventions emerged.

Exploring the minimum cognitive underpinnings required for different types of conventions further allows us to hypothesize where and under what circumstances we may expect to find conventions used by non-human animals. Taking cooperative chick rearing among birds where parents take turns at the nest as an example, we can ask whether we could in theory expect given pairs to settle on a specific daily ‘handover’ time for chick duties. These could be considered conventions if the timing is indeed at least somewhat arbitrary (i.e., switching over at 2 pm rather than 4 pm has no impact on chick rearing success), efficient (i.e., each parent can maximize its own foraging time without risking the chick being left on its own), and self-sustaining (i.e., once a specific handover time is ‘agreed’, any deviation from it will disadvantage at least one of the parents as well as the chicks). How might such a convention emerge? If we consider arriving back to the nest just as the other is preparing to leave a ‘success’, then any arrivals that miss this window could prompt an adjustment of the return time until there is a match; similarly, a parent who decides to leave before the arrival of the other may leave later in future (hunger permitting) until a window of overlap is found. This process would not require any advanced social cognition, either in terms of predicting the partner’s likely future behavior or in modelling the ‘strategy’ that the partner may be using. Although this example is highly speculative and would require longitudinal data on the development of handover times in newly mated pairs to verify, it leads us to hypothesize that conventions among non-humans in nature may emerge more frequently than currently realized.

Phase II of our study was designed to simulate the transmission of conventions from knowledgeable individuals to those ‘naïve’ to a population’s or their partner’s existing conventions. In multigenerational populations and in fission-fusion societies, for example, such naïve individuals may arrive via birth, immigration, or a reshuffling of subgroup membership. Our results showed that conventions emerged faster when one of the subjects was experienced (i.e., had learnt to solve the task via a memorized color hierarchy developed in their previous pair) but that this did not happen through the faithful transmission of the same solution that had previously emerged. Specifically, it appeared that knowledgeable individuals were able to transmit know-how (i.e., a hierarchy of colors being necessary) but not know-what (i.e., the specific ranking of colors in such a hierarchy, either as measured at the end of Phase I or as recalled by the experienced subject at the start of Phase II). Such effects may be particularly prominent in cases where interactions are purely dyadic and repeated interactions with new partners are rare or non-existent (such as in the case of the chick-rearing example discussed above) – in such cases, the experienced individual may be more willing to adapt to their partner’s preferences to facilitate convergence rather than attempt to steer the pair toward a specific hierarchy. More broadly, whether the know-how or the know-what is being transmitted may also depend on the content or the purpose of the transmission (e.g., [45,46]). Nonetheless, since we also found that our knowledgeable subjects failed to accurately recall at the start of Phase II their color hierarchies established during Phase I, it remains possible that they did not have sufficiently ‘engrained’ know-what information to transmit it accurately. Future work should examine the role of population turnover rate (affecting the proportions of naïve and knowledgeable individuals available in the population), interaction frequency (affecting the period over which the solution has to be maintained in memory without reinforcement), interaction type (whether interactions occur primarily with a fixed partner or more freely across the population), individual differences in flexibility to adjust existing preferences (affecting how likely, for example, a stubborn minority would be to accommodate population-level shifts), and the cost of failed interactions on the stability of both the form and specific content of conventional solutions.

Conventional behavior as an efficient solution to coordination problems forms the basis of many of our interactions as humans. Understanding how conventions emerge, under what conditions they are maintained stably, and what might cause them to change or disappear, can have significant implications on the functioning of our large, complex, and interconnected societies. In future, results like ours could help inform how we can best present information to individuals in a way that allows for rapid convergence to conventional solutions to coordination problems, increasing the efficiency of our interactions. Future studies should also address how factors like group size, problem context, cost of failure to coordinate, or frequency of interactions shape the formation and maintenance of conventions, and how pairwise interactions could best be structured to allow quick convergence to conventions at the population level.

Supporting information

Acknowledgments

We thank Kristin Andrews, Nicolas Claidière, and Robert Hawkins for helpful comments on an earlier draft of this manuscript. We are also grateful to Enana Jacob for help with coding subjects’ self-reported strategies.