# The dynamics of cooperation in asymmetric public goods games

## TL;DR

This study shows how inequality affects cooperation in group efforts, depending on whether the benefits of cooperation are linear or follow a threshold.

## Contribution

The paper introduces a systematic analysis of how multiple forms of inequality affect cooperation under different public goods return structures.

## Key findings

- Inequality can increase group payoffs in linear public goods games due to reciprocity-driven cooperation.
- Aligned inequality leads to worse outcomes in threshold public goods games due to conflicting expectations about fairness.
- The effect of inequality on cooperation depends on the structure of the public goods game.

## Abstract

People differ along many economic variables, including their resources and productivity. These differences affect how people cooperate. Here, we use game theory and economic experiments to explore how inequality shapes public good contributions. Results depend on the relationship between individual contributions and the returns of the public good. If the relationship is linear, inequality can promote the group’s total payoff, compared to a control without inequality. But if returns follow a nonlinear threshold function, inequality reduces total payoff. We relate these findings to the individuals’ contribution motives. For linear returns, individuals share the same motives, and contributions are mostly driven by reciprocity. Yet for nonlinear returns, inequality may lead individuals to form different expectations about which equilibrium is most fair.

When people collaborate in groups, they routinely face collective action problems: for the group effort to succeed, individuals need to cooperate despite any incentives to defect. These problems can be modeled with public goods games. To facilitate such an analysis, many studies assume the game is symmetric. Group members have the same means to cooperate (equal endowments), and contributions of different group members are equally effective (equal productivities). Studies that allow for some inequality tend to focus on one kind of inequality only. In practice, however, people can be unequal in many ways. The effect of these inequalities may in turn depend on the specific public goods game considered. To explore these issues, we combine a large-sample experiment with extensive theoretical work. We systematically vary four aspects: the group members’ endowments, their productivities, group size, and whether the public goods game exhibits linear returns or returns given by a threshold function. By exploring all four aspects, we obtain a unique dataset to explore the effect of asymmetry on cooperation. Based on this dataset, we study whether there is an advantage of “aligned inequality”: whether groups achieve a better surplus if more productive individuals have a larger endowment. For public goods games with linear returns, we find such an advantage, thereby corroborating previous research. If returns follow a threshold function, however, aligned inequality results in inferior payoffs. These results show that the effect of inequality on cooperation depends on the kind of public goods game considered.