A Logic for Strategy Updates

TL;DR

This paper introduces a dynamic logic framework for modeling strategy updates during perfect information games, addressing limitations of static strategies and proving key properties like completeness and decidability.

Contribution

It extends strategy logic to incorporate move-based strategy restrictions, providing a formal, complete, and decidable framework for dynamic strategies in game theory.

Findings

Presented a dynamic version of strategy logic

Proved completeness and decidability of the logic

Analyzed the game of centipede using the new logic

Abstract

Notion of strategy in game theory is static and presumably constructed before the game play. The static, pre-determined notion of strategies falls short analyzing perfect information games. Because, we, people, do not strategize as such even in perfect information games - largely because we are not logically omniscient, and we have limited computational power and bounded memory. In this paper, we focus on what we call move updates where some moves become unavailable during the game. Our goal here is to present a formal framework for move based strategy restrictions extending strategy logic which was introduced by Ramanujam and Simon. In this paper, we present a dynamic version of strategy logic, prove its completeness and decidability along with the decidability of the strategy logic which was an open problem so far. We also present an analysis of centipede by using our logic.