From Ehrenfeucht–Fraïssé Games to Bisimulation Games: Logical Indistinguishability and Game-Theoretic Classification

This research report studies Ehrenfeucht–Fraïssé games and bisimulation games as logical comparison games, with particular emphasis on the game-theoretic classification of bisimulation games. It connects first-order logic, modal logic, the standard translation, bisimulation invariance, and bounded logical indistinguishability, and argues that bisimulation games are structurally game-theoretic but functionally logical: their central purpose is the characterization of logical equivalence and expressiveness rather than economic payoff optimization. Version 1.0. The initial manuscript was completed in July 2026. This version is released as a research report/preprint and may be revised following academic feedback.