The Logic of Joint Ability in Two-Player Tacit Games

Peter HAWKE*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

3 Citations (Scopus)

Abstract

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: These logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality.

Original languageEnglish
Pages (from-to)481-508
Number of pages28
JournalReview of Symbolic Logic
Volume10
Issue number3
DOIs
Publication statusPublished - 1 Sep 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Association for Symbolic Logic.

Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

Keywords

  • alternating-time temporal logic
  • coalition logic
  • coordination
  • imperfect information
  • joint ability
  • Phrases logics of ability
  • strategic coordination logic
  • tacit game

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