It seems that there is no universally accepted definition of chaotic behavior of a dynamical system.

Urban traffic congestion stems from the misalignment between self-interested routing decisions and socially optimal flows. Intersections, as critical bottlenecks, amplify these inefficiencies because existing control schemes often neglect drivers' strategic behavior. Autonomous intersections, enabled by vehicle-to-infrastructure communication, permit vehicle-level scheduling based on individual requests. Leveraging this fine-grained control, we propose a non-monetary mechanism that strategically adjusts request timestamps-delaying or advancing passage times-to incentivize socially efficient routing. We present a hierarchical architecture separating local scheduling by roadside units from network-wide timestamp adjustments by a central planner. We establish an experimentally validated analytical model, prove the existence and essential uniqueness of equilibrium flows and formulate the planner's problem as an offline bilevel optimization program solvable with standard tools. Experiments on the Sioux Falls network show up to a 68% reduction in the efficiency gap between equilibrium and optimal flows, demonstrating scalability and effectiveness.

We consider the strategyproof facility location problem on a circle. We focus on the case of 5 agents, and find a tight bound for the PCD strategyproof mechanism, which selects the reported location of an agent in proportion to the length of the arc in front of it. We methodically "reduce" the size of the instance space and then use standard optimization techniques to find and prove the bound is tight. Moreover we hypothesize the approximation ratio of PCD for general odd $n$.

There are resource-allocation problems encountered in almost every aspect of human lives: from utilities such as power systems and water systems, to transportation, and office space allocation. Many analyses of resource-allocation problems employ simplistic models of the population which ignore much of the complexity of human behaviour. Notice, for example, that the demand for a resource is often non-stationary, as exemplified by the work-day morning rush hour in transportation and the existence of predictable peaks in the demand in many other domains. Notice, further, that humans may have access to only very limited amount of information, but may still consider multiple criteria, and that their appreciation of the criteria may vary over time. As an example of a particular resource-allocation problem, we introduce a model of behaviour and the related demand process, which captures both the multi-criteria aspects of the decision making and non-stationarity of the demand process. Still, we show that the distribution of agents across resources converges in distribution, for suitable means of information provision and under certain assumptions. As our running example, we consider the problems faced by transportation authorities in charge of a road network composed of a number of road segments. For each road segment, the travel time is, in principle, a time series with a data point per a vehicle passing across the road segment.

Social robotic navigation has been at the center of numerous studies in recent years. Most of the research has focused on driving the robotic agent along obstacle-free trajectories, respecting social distances from humans, and predicting their movements to optimize navigation. However, in order to really be socially accepted, the robots must be able to attain certain social norms that cannot arise from conventional navigation, but require a dedicated learning process. We propose Heuristic Planning with Learned Social Value (HPLSV), a method to learn a value function encapsulating the cost of social navigation, and use it as an additional heuristic in heuristic-search path planning. In this preliminary work, we apply the methodology to the common social scenario of joining a queue of people, with the intention of generalizing to further human activities.

Classification algorithms based on Artificial Intelligence (AI) are nowadays applied in high-stakes decisions in finance, healthcare, criminal justice, or education. Individuals can strategically adapt to the information gathered about classifiers, which in turn may require algorithms to be re-trained. Which collective dynamics will result from users' adaptation and algorithms' retraining? We apply evolutionary game theory to address this question. Our framework provides a mathematically rigorous way of treating the problem of feedback loops between collectives of users and institutions, allowing to test interventions to mitigate the adverse effects of strategic adaptation. As a case study, we consider institutions deploying algorithms for credit lending. We consider several scenarios, each representing different interaction paradigms. When algorithms are not robust against strategic manipulation, we are able to capture previous challenges discussed in the strategic classification literature, whereby users either pay excessive costs to meet the institutions' expectations (leading to high social costs) or game the algorithm (e.g., provide fake information). From this baseline setting, we test the role of improving gaming detection and providing algorithmic recourse. We show that increased detection capabilities reduce social costs and could lead to users' improvement; when perfect classifiers are not feasible (likely to occur in practice), algorithmic recourse can steer the dynamics towards high users' improvement rates. The speed at which the institutions re-adapt to the user's population plays a role in the final outcome. Finally, we explore a scenario where strict institutions provide actionable recourse to their unsuccessful users and observe cycling dynamics so far unnoticed in the literature.

We study the societal impact of pseudo-scientific assumptions for predicting the behavior of people in a straightforward application of machine learning to risk prediction in financial lending. This use case also exemplifies the impact of survival bias in loan return prediction. We analyze the models in terms of their accuracy and social cost, showing that the socially optimal model may not imply a significant accuracy loss for this downstream task. Our results are verified for commonly used learning methods and datasets. Our findings also show that there is a natural dynamic when training models that suffer survival bias where accuracy slightly deteriorates, and whose recall and precision improves with time. These results act as an illusion, leading the observer to believe that the system is getting better, when in fact the model is suffering from increasingly more unfairness and survival bias.