Path deviations outperform approximate stability in heterogeneous congestion games

We consider non-atomic network congestion games with heterogeneous players where the latencies of the paths are subject to some bounded deviations. This model encompasses several well-studied extensions of the classical Wardrop model which incorporate, for example, risk-aversion, altruism or travel time delays. Our main goal is to analyze the worst-case deterioration in social cost of a perturbed Nash flow (i.e., for the perturbed latencies) with respect to an original Nash flow. We show that for homogeneous players perturbed Nash flows coincide with approximate Nash flows and derive tight bounds on their inefficiency. In contrast, we show that for heterogeneous populations this equivalence does not hold. We derive tight bounds on the inefficiency of both perturbed and approximate Nash flows for arbitrary player sensitivity distributions. Intuitively, our results suggest that the negative impact of path deviations (e.g., caused by risk-averse behavior or latency perturbations) is less severe than approximate stability (e.g., caused by limited responsiveness or bounded rationality). We also obtain a tight bound on the inefficiency of perturbed Nash flows for matroid congestion games and homogeneous populations if the path deviations can be decomposed into edge deviations. In particular, this provides a tight bound on the Price of Risk-Aversion for matroid congestion games

Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory

Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.Comment: Appears in the 35th AAAI Conference on Artificial Intelligenc

Special Topics in Information Technology

This open access book presents thirteen outstanding doctoral dissertations in Information Technology from the Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy. Information Technology has always been highly interdisciplinary, as many aspects have to be considered in IT systems. The doctoral studies program in IT at Politecnico di Milano emphasizes this interdisciplinary nature, which is becoming more and more important in recent technological advances, in collaborative projects, and in the education of young researchers. Accordingly, the focus of advanced research is on pursuing a rigorous approach to specific research topics starting from a broad background in various areas of Information Technology, especially Computer Science and Engineering, Electronics, Systems and Control, and Telecommunications. Each year, more than 50 PhDs graduate from the program. This book gathers the outcomes of the thirteen best theses defended in 2019-20 and selected for the IT PhD Award. Each of the authors provides a chapter summarizing his/her findings, including an introduction, description of methods, main achievements and future work on the topic. Hence, the book provides a cutting-edge overview of the latest research trends in Information Technology at Politecnico di Milano, presented in an easy-to-read format that will also appeal to non-specialists

Robust Methods for Influencing Strategic Behavior

Today's world contains many examples of engineered systems that are tightly coupled with their users and customers. In these settings, the strategic and economic behavior of users and customers can have a significant impact on the performance of the overall system, and it may be desirable for an engineer to devise appropriate methods of incentivizing human behavior to improve system performance. This work seeks to understand the fundamental tradeoffs involved in designing behavior-influencing mechanisms for complex interconnected sociotechnical systems. We study several examples and pose them as problems of game design: a planner chooses appropriate ways to select or modify the utility functions of individual agents in order to promote desired behavior. In social systems these modifications take the form of monetary or other incentives, whereas in multiagent engineered systems the modifications may be algorithmic. Here, we ask questions of sensitivity and robustness: for example, if the quality of information available to the planner changes, how can we quantify the impact of this change on the planner's ability to influence behavior? We propose a simple overarching framework for studying this, and then apply it to three distinct domains: incentives for network routing, distributed control design for multiagent engineered systems, and impersonation attacks in networked systems. We ask the following questions:- What features of a behavior-influencing mechanism directly confer robustness?We show weaknesses of several existing methodologies which use pricing for congestion control in transportation networks. In response to these issues, we propose a universal taxation mechanism which can incentivize optimal routing in transportation networks, requiring no information about network structure or user sensitivities, provided that it can charge sufficiently large prices. This suggests that large prices have more robustness than small ones. We also directly compare flow-varying tolls to fixed tolls, and show that a great deal of robustness can be gained by using a flow-varying approach.- How much information does a planner need to be confident that an incentive mechanism will not inadvertently induce pathological behavior?We show that for simple enough transportation networks (symmetric parallel networks are sufficient), a planner can provably avoid perverse incentives by applying a generalized marginal-cost taxation approach. On the other hand, we show that on general networks, perverse incentives are always a risk unless the incentive mechanism is given some information about network structure.- How can robust games be designed for multiagent coordination?We investigate a setting of multiagent coordination in which autonomous agents may suffer from unplanned communication loss events; the planner's task is to program agents with a policy (analogous to an incentive mechanism) for updating their utility functions in response to such events. We show that even when the nominal game is well-behaved and the communication loss is between weakly-coupled agents, there exists no utility update policy which can prevent arbitrarily-poor states from emerging. We also investigate a setting in which an adversary attempts to influence a distributed system in a robust way; here, by understanding susceptibility to adversarial influence, we hope to inform the design of more robust network systems

Strategic decision-making in multi-agent markets: The emergence of endogenous crises and volatility

Traditional economic frameworks are built upon perfectly rational agents and equilibrium outcomes. However, during times of crises, these frameworks prove insufficient. In this thesis, we take an alternative perspective based on "Complexity Economics", relaxing the assumption of perfectly rational agents and allowing for out-of-equilibrium dynamics. While many contemporary approaches explain crises and non-equilibrium market phenomena as the rational reaction to external news, the emergence of endogenous crises remains an open question. We begin addressing this question by demonstrating how a multi-agent model of heterogeneous boundedly rational agents acting according to heuristics can reproduce and forecast key non-linear price movements in the Australian housing market, during boom and bust cycles. In order to provide foundations for such heuristic-based reasoning, we then propose a novel information-theoretic approach, Quantal Hierarchy, for modelling limitations in strategic reasoning, demonstrating how this convincingly and generically captures the decision-making of interacting agents in competitive markets outperforming existing approaches. In addition, we demonstrate how a concise generalised market model can generate important stylised facts, such as fat-tails and volatility clustering, and allow for the emergence of crises, purely endogenously. This thesis provides support to the interacting agent hypothesis, addressing a crucial question of whether crisis emergence and various stylised facts can be seen as endogenous phenomena, and provides a generic method for representing strategic agent reasoning