Knowledge and Common Knowledge of Strategies

TL;DR

This paper introduces a nuanced model of strategic knowledge, including higher-order and common knowledge, demonstrating its importance in game theory and the decidability of model checking.

Contribution

It presents a detailed framework for specifying various levels of strategic knowledge and explores their implications in games and computational problems.

Findings

Higher-order knowledge influences game outcomes as shown in Hanabi.

Common knowledge of strategies is essential for solving the consensus problem.

The paper analyzes the decidability of model checking in the proposed framework.

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.