How does inequality affect cooperation and coordination?

Collective interactions, such as teamwork, are an essential part of our daily lives. But often such interactions contain an element of a social dilemma: individuals would like their collective action to succeed, but at the same time they have an incentive to free-ride on the contributions of others. Collective action problems are particularly challenging in heterogeneous groups, in which individuals differ in their motivations and their degrees of influence. In such asymmetric scenarios, an important question is how individuals coordinate on stable cooperation.

Different fields, from economics to biology, aim to understand social behavior. Social interactions become particularly interesting in the presence of inequalities. In real-life groups, individuals often differ significantly in what they can do, and what consequences their actions have. In the presence of such inequalities, several questions arise naturally. For example, how do different kinds of inequality affect the way people cooperate? And how do they affect how people form expectations about others’ behaviors? Recently, Xiaomin Wang, Marta C. Couto, and Christian Hilbe from the Research Group Dynamics of Social Behaviour based at the Max Planck Institute for Evolutionary Biology studied these questions, in a collaboration with a team of researchers from Beijing Normal University. To do so, they use human experiments and mathematical models of game theory. The main findings show that when people are unequal, there can be a mismatch in prior expectations. This mismatch can then further delay the time it takes people to coordinate on optimal collective outcomes. However, on the bright side, people’s preference for fairness is salient, even in the presence of exogenous inequality.

To explore coordination in heterogeneous groups, the researchers considered the following game. Two players have an initial endowment (i.e. their wealth). Both of them need to simultaneously decide how much of their endowment to contribute to a common pot. Each contribution is multiplied by a productivity factor (i.e. the efficiency of their contributions to the public good). If the collective amount is equal to, or above, a pre-defined value (the threshold), all players receive a reward (the shared benefit). The reward is always the same, no matter whether the group reaches the threshold exactly or surpasses it. As a consequence, this is a coordination problem: the two players are incentivized to coordinate either on contributing nothing or to contribute such that the threshold is exactly met. Aiming for the threshold is risky: when the players’ total contributions do not meet the threshold, they lose any contribution already put forward. At the same time, meeting the threshold is better than contributing nothing as players get a worthy reward. Still, even if players aim to reach the threshold, there are many ways in which they can do so, as the two players can contribute more or less equally. Notably, each player would always prefer the co-player to contribute a larger share. Thus, the question is: on which of these outcomes do people eventually coordinate?

Observation of human behaviour

To observe real human behavior, the researchers recruited students to play this coordination game in a computer lab for several rounds against the same co-player (see figure). The researchers found that most pairs learn to coordinate on a cooperative outcome (that is, they eventually meet the threshold). Moreover, when players are fully equal, they quickly coordinate on contributing equal amounts.

However, when players have different endowments, they take longer to reach the threshold, and sometimes they miss it altogether. In games with asymmetric endowments, there are different heuristics that individuals may use for their decisions. For example, they might consider it fair to contribute the same absolute amount as their interaction partner. Alternatively, they might consider it fair if both individuals contribute the same proportion of their endowment. Once participants disagree in their expectations of what to do in this game, this can lead to an initial mismatch between the players' contributions. This initial mismatch in turn leads to significantly more pairs of players failing to attain the threshold.

Interestingly, the researchers did not observe such coordination failures when participants differed in their productivities instead of their endowments. Here, participants simply tend to contribute the same amount, irrespective of how productive these contributions are. These results suggest that people dismiss a more efficient outcome (where the more productive player contributes more and the collective payoff is larger) in favor of an egalitarian one. Surprisingly, individuals agree on this outcome quite fast, even those players who would benefit from playing more efficiently.

The researchers also analyzed several mathematical models that could explain the observed regularities. When models assume the player’s initial behavior to be random, the corresponding models provide a poor fit to the empirical results. This is to say that if we know little about what people might do to start with, it is hard to predict their future actions. However, if we do have some knowledge of people’s initial tendencies, models give more accurate predictions. This finding confirms that whatever people do in the first rounds of a coordination game highly affects the further fate of the encounter.

This work was published by Philosophical Transactions of the Royal Society B in a thematic issue called “Half a century of evolutionary games: a synthesis of theory, application, and future direction”.