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Life sciences · Preprint
arXiv · August 10, 2026
Raises a question worth testing. It does not answer one.
This is a theoretical tutorial introducing learning in games, covering regret bounds in adversarial bandits, equilibrium convergence in zero-sum games, and connections between Nash equilibria and learning dynamics. It presents mathematical frameworks and proofs without empirical validation and is intended as an educational entry point to the literature rather than as evidence for a specific clinical or practical claim.
Preprint.
Presents regret bounds for regularized learning in adversarial multi-armed bandits Describes ergodic equilibrium convergence for zero-sum games under fictitious play Establishes folk theorem linking Nash equilibria to attracting points of regularized learning
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The source did not state who this applies to in practice.
This is a theoretical tutorial paper presenting mathematical frameworks for learning in games without empirical validation, clinical outcomes, or real-world application data.
Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.
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This note aims to serve as an entry point to the literature on learning in games, a topic with significant theoretical appeal and a wide range of applications -- from machine learning and data science to economics and beyond. Our presentation is structured around two complementary viewpoints: We first consider a single agent -- the learner -- engaged in a sequential decision process in an unknown, non-stationary, and possibly adversarial environment. We then examine what happens when the environment is shaped by the decisions of several interacting agents, not necessarily aware of each other's actions or goals, and all seeking to improve their individual rewards. In this general context, we examine a family of regularized learning policies based on best-responding to the past history of play, up to a regularization penalty intended to encourage exploration and prevent over-commitment to suboptimal choices. In the single-agent setting, we present some basic regret bounds for regularized learning in adversarial multi-armed bandits; in the multi-agent setting, we describe an ergodic equilibrium convergence result for zero-sum games in the spirit of classical results on fictitious play, as well as a "folk theorem" linking strategic and dynamic notions of stability -- Nash equilibria and attracting points of regularized learning, respectively. We pay special attention to the information available to the players and, through a unified analysis framework, we study both oracle- and payoff-based (bandit) methods. Our goal is to provide a coherent and comprehensible -- albeit, by necessity, not comprehensive -- account of some recent ideas in the field, and to discuss their implications for the study of rationality.
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