Institutions allow cooperation to persist when reciprocity and reputation provide insufficient incentives. Yet how they do so remains unclear, especially given that institutions are themselves a form of cooperation. To solve this puzzle, we develop a mathematical model of reputation-based cooperation in which two social dilemmas are nested within one another. The first dilemma, characterized by high individual costs or insufficient monitoring, cannot be solved by reputation alone. The second dilemma, an institutional collective action, involves individuals contributing to change the parameters of the first dilemma in a way that incentivizes cooperation. Our model demonstrates that this nested architecture creates a leverage effect. While insufficient on its own to incentivize cooperation in the first dilemma, reputation incentivizes contributions to the institutional collective action which, in turn, strengthen the initially weak incentives for cooperation in the first dilemma. Just as a pulley system transforms minimal muscular strength into significant lifting capability, institutions act as cooperative pulleys, transforming initially weak reputational incentives into powerful drivers of cooperative behavior. Based on these results, we suggest that institutions have developed as social technologies, designed by humans to exploit this social leverage effect, just as material technologies are designed to exploit physical laws.

To demonstrate their commitment, for instance during wartime, members of a group will sometimes all engage in the same ruinous display. Such uniform, high-cost signals are hard to reconcile with standard models of signaling. For signals to be stable, they should honestly inform their audience; yet, uniform signals are trivially uninformative. To explain this phenomenon, we design a simple model, which we call the signal runaway game. In this game, senders can express outrage at non-senders. Outrage functions as a second-order signal. By expressing outrage at non-senders, senders draw attention to their own signal, and benefit from its increased visibility. Using our model and a simulation, we show that outrage can stabilize uniform signals, and can lead signal costs to run away. Second-order signaling may explain why groups sometimes demand displays of commitment from all their members, and why these displays can entail extreme costs.

Many evolutionary models explain why we cooperate with non-kin, but few explain why cooperative behaviour and trust vary. Here, we introduce a model of cooperation as a signal of time preferences, which addresses this variability. At equilibrium in our model (i) future-oriented individuals are more motivated to cooperate, (ii) future-oriented populations have access to a wider range of cooperative opportunities, and (iii) spontaneous and inconspicuous cooperation reveal stronger preference for the future, and therefore inspire more trust. Our theory sheds light on the variability of cooperative behaviour and trust. Since affluence tends to align with time preferences, results (i) and (ii) explain why cooperation is often associated with affluence, in surveys and field studies. Time preferences also explain why we trust others based on proxies for impulsivity, and, following result (iii), why uncalculating, subtle and one-shot cooperators are deemed particularly trustworthy. Time preferences provide a powerful and parsimonious explanatory lens, through which we can better understand the variability of trust and cooperation.