Knowledge and Common Knowledge of Strategies
Borja Sierra Miranda, Thomas Studer
TL;DR
The paper introduces a fine-grained epistemic framework for knowledge of strategies built on information perspectives $\mathrm{I}$ over concurrent game structures $\mathcal{G}$, enabling explicit representation of first-order, higher-order, and common knowledge of strategies. It shows how higher-order knowledge influences strategic reasoning in Hanabi and proves that common knowledge of strategies is necessary to solve the binary consensus problem. Decidability of model checking is established for the base language $\mathcal{L}$ (excluding common knowledge operators) via a bounded-depth argument using $\mathsf{kd}(\phi)$, with open questions about extending results to $\mathcal{L}^{\mathsf{C}}$ and to strategy-logic formulations. The work advances formal understanding of strategic reasoning under imperfect information and sets directions for CK-aware model checking and strategy-centric logics.
Abstract
Most existing work on strategic reasoning simply adopts either an informed or an uninformed semantics. We propose a model where knowledge of strategies can be specified on a fine-grained level. In particular, it is possible to distinguish first-order, higher-order, and common knowledge of strategies. We illustrate the effect of higher-order knowledge of strategies by studying the game Hanabi. Further, we show that common knowledge of strategies is necessary to solve the consensus problem. Finally, we study the decidability of the model checking problem.