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Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome of an uncertain event, is an increasingly popular way for robots to act under uncertainty. In this work we take a game-theoretic perspective on contingency planning, tailored to multi-agent scenarios in which a robot’s actions impact the decisions of other agents and vice versa. The resulting contingency game allows the robot to efficiently interact with other agents by generating strategic motion plans conditioned on multiple possible intents for other actors in the scene. Contingency games are parameterized via a scalar variable which represents a future time when intent uncertainty will be resolved. By estimating this parameter online, we construct a game-theoretic motion planner that adapts to changing beliefs while anticipating future certainty. We show that existing variants of game-theoretic planning under uncertainty are readily obtained as special cases of contingency games. Through a series of simulated autonomous driving scenarios, we demonstrate that contingency games close the gap between certainty-equivalent games that commit to a single hypothesis and non-contingent multi-hypothesis games that do not account for future uncertainty reduction. 

Abstract Extreme weather events have devastating impacts on human health, economic activities, ecosystems, and infrastructure. It is therefore crucial to anticipate extremes and their impacts to allow for preparedness and emergency measures. There is indeed potential for probabilistic subseasonal prediction on time scales of several weeks for many extreme events. Here we provide an overview of subseasonal predictability for case studies of some of the most prominent extreme events across the globe using the ECMWF S2S prediction system: heatwaves, cold spells, heavy precipitation events, and tropical and extratropical cyclones. The considered heatwaves exhibit predictability on time scales of 3–4 weeks, while this time scale is 2–3 weeks for cold spells. Precipitation extremes are the least predictable among the considered case studies. ­Tropical cyclones, on the other hand, can exhibit probabilistic predictability on time scales of up to 3 weeks, which in the presented cases was aided by remote precursors such as the Madden–Julian oscillation. For extratropical cyclones, lead times are found to be shorter. These case studies clearly illustrate the potential for event-dependent advance warnings for a wide range of extreme events. The subseasonal predictability of extreme events demonstrated here allows for an extension of warning horizons, provides advance information to impact modelers, and informs communities and stakeholders affected by the impacts of extreme weather events.