A collective-risk social dilemma arises when a group must cooperate to reach a common target in order to avoid the risk of collective loss while each individual is tempted to free-ride on the contributions of others. In contrast to the prisoners' dilemma or public goods games, the collective-risk dilemma encompasses the risk that all individuals lose everything. These characteristics have potential relevance for dangerous climate change and other risky social dilemmas. Cooperation is costly to the individual and it only benefits all individuals if the common target is reached. An individual thus invests without guarantee that the investment is worthwhile for anyone. If there are several subsequent stages of investment, it is not clear when individuals should contribute. For example, they could invest early, thereby signaling their willingness to cooperate in the future, constantly invest their fair share, or wait and compensate missing contributions. To investigate the strategic behavior in such situations, we have simulated the evolutionary dynamics of such collective-risk dilemmas in a finite population. Contributions depend individually on the stage of the game and on the sum of contributions made so far. Every individual takes part in many games and successful behaviors spread in the population. It turns out that constant contributors, such as constant fair sharers, quickly lose out against those who initially do not contribute, but compensate this in later stages of the game. In particular for high risks, such late contributors are favored.

In collective-risk dilemmas, a group needs to collaborate over time to avoid a catastrophic event. This gives rise to a coordination game with many equilibria, including equilibria where no one contributes, and thus no measures against the catastrophe are taken. In this game, the timing of contributions becomes a strategic variable that allows individuals to interact and influence one another. Herein, we use evolutionary game theory to study the impact of strategic timing on equilibrium selection. Depending on the risk of catastrophe, we identify three characteristic regimes. For low risks, defection is the only equilibrium, whereas high risks promote equilibria with sufficient contributions. Intermediate risks pose the biggest challenge for cooperation. In this risk regime, the option to interact over time is critical; if individuals can contribute over several rounds, then the group has a higher chance to succeed, and the expected welfare increases. This positive effect of timing is of particular importance in larger groups, where successful coordination becomes increasingly difficult.

Mitigating the detrimental effects of climate change is a collective problem that requires global cooperation. However, achieving cooperation is difficult since benefits are obtained in the future. The so-called collective-risk game, devised to capture dangerous climate change, showed that catastrophic economic losses promote cooperation when individuals know the timing of a single climatic event. In reality, the impact and timing of climate change is not certain; moreover, recurrent events are possible. Thus, we devise a game where the risk of a collective loss can recur across multiple rounds. We find that wait and see behavior is successful only if players know when they need to contribute to avoid danger and if contributions can eliminate the risks. In all other cases, act quickly is more successful, especially under uncertainty and the possibility of repeated losses. Furthermore, we incorporate influential factors such as wealth inequality and heterogeneity in risks. Even under inequality individuals should contribute early, as long as contributions have the potential to decrease risk. Most importantly, we find that catastrophic scenarios are not necessary to induce such immediate collective action.