Reinforcement learning and game theory describe the same object from two sides. Game theory says what a rational outcome of a strategic interaction is; reinforcement learning says how an agent could reach one through experience. The two literatures nevertheless keep separate vocabularies for identical structures, and the treatments that bridge them present the correspondence as analogy rather than theorem. This monograph supplies the theorems.
Games as Markov Decision Processes in Three Senses
A game is a Markov decision process in three distinct senses, and every table entry is labelled with the one that applies: a definitional identity, an exact reduction carried by a value- and solution-preserving map, or a structural analogy that fails under identifiable conditions.
Correspondence Between Game Classes and RL Decision-Theoretic Models
We take every standard class of game and identify for each the decision-theoretic model that reinforcement learning already studies under another name. The classes include:
- normal-form
- repeated
- stochastic
- partially observable
- extensive-form with imperfect information
- Bayesian</