Computational Modelling for Combinatorial Game Strategies

TL;DR

This paper introduces a logic-based computational model using algebraic specification to determine winning strategies in finite combinatorial games, enabling experimental mathematics approaches.

Contribution

It presents a novel equational logic-based framework for analyzing combinatorial game strategies, implemented in equational programming systems.

Findings

Effective method for establishing winning strategies

Demonstrated with case studies

Enables experimental mathematics in game theory

Abstract

We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from algebraic specification, and it can be executed by equational programming systems such as those from the OBJ-family. We show how this provides a form of experimental mathematics for strategy problems involving combinatorial games. We do this by defining general methods and by illustrating these with case studies.