Varied real world systems such as transportation networks, supply chains and energy grids present coordination problems where many agents must learn to share resources. It is well known that the independent and selfish interactions of agents in these systems may lead to inefficiencies, often referred to as the ‘Price of Anarchy’. Effective interventions that reduce the Price of Anarchy while preserving individual autonomy are of great interest. In this paper we explore recommender systems as one such intervention mechanism. We start with the Braess Paradox, a congestion game model of a routing problem related to traffic on roads, packets on the internet, and electricity on power grids. Following recent literature, we model the interactions of agents as a repeated game between Q -learners, a common type of reinforcement learning agents. This work introduces the Learning Dynamic Manipulation Problem, where an external recommender system can strategically trigger behavior by picking the states observed by Q -learners during learning. Our computational contribution demonstrates that appropriately chosen recommendations can robustly steer the system towards convergence to the social optimum, even for many players. Our theoretical and empirical results highlight that increases in the recommendation space can increase the steering potential of a recommender system, which should be considered in the design of recommender systems. • Agents play a repeated congestion game while a recommender system influences them. • Agents are independent Q-learners. • The recommender system provides signals to optimize system efficiency. • Recommendations are modeled as states that are selected by the external recommender. • Recommendations steer agents from the Nash equilibrium towards the social optimum.

The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence. Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness.

The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence. Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness.