To study the problem of group identity change in strategic environments, I start by setting out a theoretical model in which there is a population of individuals who are exogenously assigned a group identity, either group ● (the majority) or group ▲ (the minority). Individuals decide with whom to interact (their network of connections) and then chooses between two actions: p or b . Everyone prefers to coordinate on one action but individuals differ in the action they prefer depending on their group identity. Those in group ● prefer action p and those in group ▲ prefer action b . The key feature of the model is that, prior to forming their network and choosing between the two actions, individuals can choose whether to keep or change their group identity. The cases where individuals do not change their groups (either because it is not possible or because it is too costly) are included as part of the equilibrium characterization.
The theoretical analysis reveals that among the equilibria when group identities are fixed, there is a segregated outcome where those in group ● form a cluster between them and choose p , while those in group ▲ form a separate cluster and choose b . However, in equilibrium, there is also an integrated outcome where players form a complete network and all choose p . This means that the ▲’s end up choosing the action they like less. In fact, this setting where the minority conforms to the majority is the efficient outcome. On the other hand, when group identities are fluid (can be changed) all players select their preferred action and connect with others choosing the same. In this case, the complete network is an equilibrium only when al players choose to have the same group identity. That is, when no player chooses the action she likes less. Otherwise, such players would be better off changing their group identity to match their chosen action. this is the efficient equilibrium outcome.
Thus, the endogenous change of group identities works as a strong commitment device that shapes equilibrium outcomes from the start, given that actions and connections must correspond to preferences in equilibrium.
A final theoretical consideration is grounded on the assumption that players have preferences for consistency: categories and attributes correlate. In such cases, depending on how costly it is to interact with an inconsistent counterpart, a consistent player may not connect with inconsistent others, even if they identify with the same group. Therefore, in equilibrium, an consistent player is worse off changing her group and outcomes are as in the case where group identities were fixed.
I conduct laboratory experiments to better understand how players choose their groups, their connections and their actions both in settings were group identities are fixed or fluid. Each treatment has 4 parts: group names, fixed groups, fluid groups, and group allocations. In all of them, participants interact in the same group of 7 subjects. There are 4 ● and 3 ▲.
In part 1, names, participants interact in a simple group cohesion task. Each participant is informed whether she is assigned to group ● or ▲. Then, participants have two minutes to chat with the other members of their assigned group and choose a name for their group out of a list of three possible names (e.g., lions, elephants, zebras). If they all choose the same name each earns a monetary benefit. If at least one chooses a different name they do not receive any benefit and the name will be randomly assigned. Solving such a simple coordination task as a group, using chats, has been shown to enhance group cohesion in multiple experiments, which allows me to reinforce group identification.
In part 2 fixed, participants play a coordination game in which group identities cannot be changed repeatedly for 10 rounds. The 4 subjects in group ● prefer action p (the majority) and 3 subjects in group ▲ prefer action b (the minority). Both theoretical and empirical evidence has consistently indicated that in these settings strong communities are likely to be formed, where people are more connected with those sharing a common identity than with others (Goyal et al., 2018; Jackson and Storms, 2018). These social structures are difficult to alter by single individuals, given that each individual has limited influence on the group (Baronchelli, 2018; Hoff and Stiglitz, 2011). The consistent empirical finding observed in previous studies (Ellwardt et al., 2016; Goyal et al., 2018) is that players choose the segregated outcome and end up in a less efficient equilibrium that they would have had they integrated and conformed to a single action.
In part 3, fluid, players can choose their group identity in each round before choosing their action. Thus, the proportion of the majority/minority does not need to be as in fixed. In this setup integration can be achieved by changing groups instead of by conforming on a disliked behavior. This means that it is optimal for minority players (the ▲) to change their group identities and join the majority (the ●). This would result in the integrated equilibrium outcome. However, if players have preferences for consistency, it is not clear that the majority would welcome (connect with) the newcomers. This would result in the persistence of the segregated equilibrium outcome. Following up on this, I explore the idea that costly change and visibility prevent individuals from endogenously changing their identities, thus perpetuating inefficient group dynamics.