A New Game Equivalence and its Modal Logic

TL;DR

This paper introduces a refined concept of game equivalence based on basic powers, capturing strategic interaction details, and develops a corresponding modal logic framework for analyzing such games.

Contribution

It proposes a new notion of game equivalence based on basic powers and develops a modal logic and algebraic framework for this refined concept.

Findings

A new representation theorem for basic powers

Development of instantial neighborhood game logic

Extension to a new game algebra and dynamic game logic

Abstract

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more finegrained notion of equality of "basic powers" which record what players can force plus what they leave to others to do, a crucial feature of interaction. This notion is closer to game-theoretic strategic form, as we explain in detail, while remaining amenable to logical analysis. We determine the properties of basic powers via a new representation theorem, find a matching "instantial neighborhood game logic", and show how our analysis can be extended to a new game algebra and dynamic game logic.