Strategy Composition in Dynamic Games with Simultaneous Moves

Sometimes, in dynamic games, it is useful to reason not only about the existence of strategies for players, but also about what these strategies are, and how players select and construct them. We study dynamic games with simultaneous moves, repeated normal form games and show that this reasoning can be carried out by considering a single game, and studying composition of “local” strategies. We study a propositional modal logic in which such reasoning is carried out, and present a sound and complete axiomatization of the valid

[1]  Sujata Ghosh Strategies made explicit in Dynamic Game Logic , 2008 .

[2]  Eric Bennett Rasmusen Readings in games and information , 2001 .

[3]  R. Ramanujam,et al.  Strategies in Games: A Logic-Automata Study , 2010, ESSLLI.

[4]  Andreas Herzig,et al.  Using STIT Theory to Talk About Strategies , 2015, Models of Strategic Reasoning.

[5]  Jan M. Broersen,et al.  A stit-Logic for Extensive Form Group Strategies , 2009, 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology.

[6]  Wojciech Jamroga,et al.  Logics for Reasoning About Strategic Abilities in Multi-player Games , 2015, Models of Strategic Reasoning.

[7]  Thomas Ågotnes,et al.  Action and Knowledge in Alternating-Time Temporal Logic , 2006, Synthese.

[8]  Michael Wooldridge,et al.  Alternating-time temporal logic with explicit strategies , 2007, TARK '07.

[9]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[10]  Johan van Benthem,et al.  In Praise of Strategies , 2012, Games, Actions and Social Software.

[11]  Jan M. Broersen,et al.  CTL.STIT: enhancing ATL to express important multi-agent system verification properties , 2010, AAMAS.

[12]  J. Horty Agency and Deontic Logic , 2001 .

[13]  Cees Witteveen,et al.  A Modal Characterization of Nash Equilibrium , 2003, Fundam. Informaticae.

[14]  Johan van Benthem,et al.  Extensive Games as Process Models , 2002, J. Log. Lang. Inf..

[15]  Guifei Jiang Representing and Reasoning about Game Strategies , 2015, AAMAS.

[16]  Ramaswamy Ramanujam,et al.  Dynamic Logic on Games with Structured Strategies , 2008, KR.

[17]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 1999 .

[18]  Giacomo Bonanno Branching Time Logic, Perfect Information Games and Backward Induction , 1998 .

[19]  Wojciech Jamroga,et al.  A logic for strategic reasoning , 2005, AAMAS '05.

[20]  Krishnendu Chatterjee,et al.  Strategy logic , 2007, Inf. Comput..