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THE LOGIC OF JOINT ABILITY IN TWO-PLAYER TACIT GAMES

Published online by Cambridge University Press:  27 March 2017

PETER HAWKE
PETER HAWKE*
Affiliation:
Stanford University, Department of Philosophy
*
*DEPARTMENT OF PHILOSOPHY STANFORD UNIVERSITY 450 SERRA MALL STANFORD, CA 94305, USA E-mail: phawke@stanford.edu
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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.

Keywords

03: Mathematical logic and foundations 91: Game theoryeconomicssocial and behavioral scienceslogics of abilitystrategic coordination logicalternating-time temporal logiccoalition logiccoordinationjoint abilityimperfect informationtacit game
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 3 , September 2017 , pp. 481 - 508
Copyright
Copyright © Association for Symbolic Logic 2017 

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