diversity in academic collaboration is crucial for increased research quality, productivity, & innovation, leading to better problem-solving, increased creativity, and greater access to expertise ( III, V, VI, VII ). despite these benefits, discrimination against minority groups is widespread in scientific networks, but why might this happen? our initial reaction is often to think that biases, both conscious & unconscious, affect how researchers choose to collaborate with one another & can therefore lead to discriminatory interactions. while these biases do exist & can greatly affect the experiences of minority researchers, might there be something else happening that is affecting the emergence, evolution, & persistence of discriminatory norms in academia?

combining this line of questioning with my methodological interests of agent-based modeling (abm), i utilized game-theoretic models to simulate interaction & collaboration amongst researchers in an academic population to gain insight into the emergence & persistence of discriminatory patterns of behavior, or norms, in academic collaboration networks. abm refers to a way to simulate how individual agents, like the researchers of interest, interact within a system. here, a game-theoretic model specifically refers to the integration of a commonly used cooperative bargaining game called the nash demand game into an agent-based model.

the nash demand game allows us to study how people choose to bargain & divide shared resources. imagine if two (at its simplest case, we will focus on the game being played between two players but it can be applied to more) people have a cake made up of ten slices sitting between them that they are asked to share. each person must independently decide how much of the cake they want to ask for & will simultaneously state their demands to one another, meaning they cannot first hear how much of the cake the other person will demand before making their demand. since the cake is a finite resource with only ten slices, if the total simultaneous demand the players make is equal to or less than the number of slices of cake available, they both get what they asked for. however, if the players demands are incompatible and their combined demands are greater than the number of slices available, neither player receives what they asked for.

the nash demand game illustrates the importance of making coordinated, reasonable demands in an effort to create successful outcomes for all parties involved. in the context of my research specifically, you can think of the cake as being replaced by the total amount of payoff, or credit, that an academic collaboration produces. the demands for slices of cake can then be equated to how much of that total collaboration payoff each researcher in a collaboration asks for. think of this as a scenario in which research collaborators are negotiating for something like authorship order or any other proxy for recognition (number of slices) from a collaboration (the whole cake). as such, the nash demand game is a great representation of how bargaining occurs in collaborations. a game-theoretic model simply refers to a simulated network of researchers, or agents, that are interacting and playing a version of the nash demand game with each other to represent their collaborations.

finally, this research also applies theory extended from evolutionary biology related to interactions between groups of people. since this model is specifically interested in determining how discriminatory norms may develop & persist, each researcher in the model population is randomly assigned a social identity label of either belonging to a minority or majority group. this label is not specified but can be thought of as anything that is a marker of group identity that can lead to bias in interactions such as race, sex, gender, religion, etc. the development of nash demand game norms (or how the majority of people in each identity group decide to interact with people within their own identity group & outside their own identity group) across each of these groups is of particular interest. you may remember that i mentioned that is natural to think discriminatory norms may develop because of conscious or unconscious biases between collaborators, but could something else be at play? specifically, think of the biological red queen hypothesis which refers to a constant evolutionary arms race. according to this hypothesis, when two species are in competition, they will constantly adapt to maintain their standing against their competitors in an effort to avoid extinction ( VIII ).

this study is interested in the related cultural red king effect, which extends the red queen hypothesis to cultural studies and argues that the speed at which two groups learn & adapt relative to one another is critical to their development. specifically, the group that learns & adapts more slowly can inadvertently gain an advantage over the other ( I, II ). if minority label researchers make up a smaller portion of the overall population than majority label researchers, minority researchers will be more likely to interact with a majority researcher than with another minority researcher due to group size alone when randomly selecting a collaborator from the overall population. as such, the minority group would be learning how to interact with & adapt to the majority group quickly. conversely, since the majority group would interact with minority researchers less frequently, they would be the slower learning group. could the minority group be learning to play it safe & demand less quickly while the majority group learns to exploit these demands leading to the development of a discriminatory norm without the introduction of bias & due to just group size & differential rates of interaction & learning alone.

this research both replicated & extended game-theoretic models from rubin and o'connor (2018). it was comprised of three models total. you can learn more about the development of models here! building & validating these types of models can be difficult. as a researcher building these models, you are responsible for justifying why certain mechanisms were implemented in the way they were & to ensure that the implementation of these mechanisms does not introduce bias into results. as such, models one & two, while providing useful insights into the questions of interest, were mainly created to rigorously test fundamental model mechanics before they were incorporated into the larger, main model of interest ( model three ) to ensure result accuracy & validity.

the first model focused on the emergence of discriminatory norms within fixed collaboration networks. the model in this first study was intended to be a very base model that i could then build off of for the next studies. as such, here, a fixed network refers to a network in which collaboration structure, or the connections between the agents in the simulation, remained constant & unchanging throughout a run of the model. collaborative relationships did not form, break, or evolve as this network had its connections pre-established at the outset of the model. each network simulation involved between twenty & one hundred agents, or researchers, randomly assigned either a majority or minority group label based on the varying minority percentage parameter which represented how much of the overall population was to be made up of minority label researchers. each agent held two bargaining strategies, one for in-group collaborations ( minority researchers interacting with minority researchers; majority researchers interacting with majority researchers ) & one for out-group collaborations (minority researchers interacting with majority researchers & vice-versa ). these strategies were initially randomly assigned to each agent but they were able to update their strategies throughout each run of the model using the myopic best response method to maximize credit payoff. in this method, each researcher looks back upon their last interaction and determines what demand strategy would have given them the best collaboration credit payoff in their last collaboration. depending on the identity label of the person they had their last interaction with, the researcher will then adopt that demand strategy for that particular group to use in their next interaction with someone of that group. the credit demand strategies held by researchers could be to demand low credit, medium or fair credit, or high credit from their collaborators.

the second model built off of this base model, instead exploring a dynamic network in which collaborative relationships could form, break, or evolve. however, in this particular model, discriminatory norms were already in place before the model run even began. each simulation started with no pre-existing links among between ten & one hundred agents, with discriminatory credit demands pre-assigned (the majority group was initialized to demand high from minorities, the minority group was initialized to demand low from majorities, & in-group interactions were initialized to be fair). researchers could form or break links based on potential credit payoffs & were capped with a maximum number of collaborations that they could partake in at any given time.

finally, model three joined the mechanics tested in models one & two to investigate the coevolution of discriminatory norms & network structure. an empty network of one hundred agents was initialized with each agent holding a random, initial bargaining strategy that they could then use myopic best response to update at each time step ( as tested in model one ). each agent was also given the opportunity to update who they wanted to keep as collaborator as well ( as tested in model two ).

runs of model one produced results consistent with those published by rubin and o'connor (2018). this replication showed that while in-group collaborations typically converged to fair demands, out-group collaborations often resulted in fair division but also significantly resulted in majority discrimination, with a majority of the majority label group settling on making high demands of minority researchers when demanding credit. critically, as minority group size decreased, the level of discrimination faced by minorities increased, aligning with predictions made by the cultural red king effect.

runs of model two showed that under fixed discriminatory norms, homophily, or the tendency for individuals to associate with ( or in this model, collaborate with ) those similar to themselves, increased over time. once researchers began to hit the maximum number of collaborative links they could hold at a time, they began to prioritize within-group collaborations to avoid discrimination indicating that discriminatory norms did drive researchers to form collaborative subclusters predominantly with members of their own social identity group. this effect was especially prominent in minority researchers

results from model three, which investigated the coevolution of discrimination and network structure, were slightly more varied as compared to models one & two. trends from model one, such as increasing majority discrimination with decreasing minority group size, were observed again. as in model two, a trend towards increased homophily was observed as well, resulting in partially segregated networks. the outcomes for bargaining strategies showed more variation however. majority groups were nearly equally likely to demand fair or high credit from minorities while minorities themselves often demanded high credit from majorities and sometimes settled on demanding fair credit instead. overall, runs often resulted in partially segregated networks & a prevalence of discriminatory credit division norms, with an implied increase in homophily as discrimination increased. these results were incredibly interesting & may perhaps highlight issues related to model replication as well as the nuances of model building.

this replication & extensions of rubin and o'connor's models deepen our understanding of how discrimination operates within academic collaboration networks. the question posed earlier of what other factors besides outright bias could lead to discrimination in social networks is partially answered. these findings consistently displayed that smaller minority groups were more susceptible to discrimination. existing discriminatory norms within a network also led to increased homophily, pushing researchers to choose to collaborate with others of similar social identities to themselves. this finding highlights the dangers of introducing minority researchers into collaboration networks in which some sort of implicit, discriminatory norm already exists. increased homophily can have negative consequences, such as limiting the spread of information, promoting redundant knowledge, decreasing opportunities for joint knowledge production, and potentially leading to publications in lower-impact journals with fewer citations for these researchers ( IV, V ) which could ultimately affect career success & trajectory. this work highlights the complex interplay between social identity, bargaining strategies, & network structure in shaping the collaborative landscape of academia, emphasizing the challenges faced by minority researchers which can create significant barriers in career progression.

references:

I. bergstrom & lachmann, 2003 — the red king effect : when the slowest runner wins the coevolutionary race

II. bruner, 2019 — miinority ( dis ) advantage in population games

III. bukvova, 2010 — studying research collaboration : a literature review

IV. de miranda grochocki & cabello, 2023 — research collaboration networks in maturing academic environments

V. freeman & huang, 2014 — collaboration : strength in diversity

VI. leahey, 2016 — from sole investigator to team scientist : trends in the practice & study of research collaboration

VII. rubin & o’connor, 2018 — discrimination & collaboration in science

VIII. van valen, 1973 — the red queen

relevant resources:

I. learn more about homophily