Epistemic foundations for backward induction: an overview

In this survey we analyze, and compare, various sufficient epistemic conditions for backward induction that have been proposed in the literature. To this purpose we present a simple epistemic base model for games with perfect information, and translate the different models into the language of this base model. As such, we formulate the various sufficient conditions for backward induction in a uniform language, which enables us to explictly analyze their differences and similarities.

[1]  Pierpaolo Battigalli,et al.  On Rationalizability in Extensive Games , 1997 .

[2]  Ken Binmore,et al.  Modeling Rational Players: Part II , 1987, Economics and Philosophy.

[3]  Wlodek Rabinowicz,et al.  Grappling With the Centipede: Defence of Backward Induction for BI-Terminating Games , 1998, Economics and Philosophy.

[4]  R. Aumann.  Backward induction and common knowledge of rationality , 1995 .

[5]  Ken Binmore,et al.  Modeling Rational Players: Part I , 1987, Economics and Philosophy.

[6]  Dov Samet,et al.  Hypothetical Knowledge and Games with Perfect Information , 1996 .

[7]  John Broome,et al.  Backwards induction in the centipede game , 1999 .

[8]  P. Reny.  Common Belief and the Theory of Games with Perfect Information , 1993 .

[9]  Eyal Winter,et al.  A Necessary and Sufficient Epistemic Condition for Playing Backward Induction , 1997 .

[10]  Pierpaolo Battigalli,et al.  Strong Belief and Forward Induction Reasoning , 2002, J. Econ. Theory.

[11]  Robert Stalnaker.  Knowledge, Belief and Counterfactual Reasoning in Games , 1996, Economics and Philosophy.

[12]  J. Mycielski.  Games with perfect information , 1992 .

[13]  Thorsten Clausing,et al.  Doxastic Conditions for Backward Induction , 2003 .

[14]  Ken Binmore,et al.  Modeling rational players I , 1987 .

[15]  G. Bonanno.  Rational beliefs in extensive games , 1992 .

[16]  Philip J. Reny,et al.  Rationality in Extensive-Form Games , 1992 .

[17]  A. Quesada,et al.  Belief system foundations of backward induction , 2002 .

[18]  Antonio Quesada,et al.  From Common Knowledge of Rationality to Backward Induction , 2003, IGTR.

[19]  Joseph Y. Halpern.  Substantive Rationality and Backward Induction , 1998, Games Econ. Behav..

[20]  R. Aumann.  On the Centipede Game , 1998 .

[21]  David Pearce.  Rationalizable Strategic Behavior and the Problem of Perfection , 1984 .

[22]  Andrés Perea,et al.  Sequential and quasi-perfect rationalizability in extensive games , 2005, Games Econ. Behav..

[23]  Elchanan Ben-Porath,et al.  Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games , 1997 .

[24]  H. Keisler,et al.  ADMISSIBILITY IN GAMES , 2008 .

[25]  R. Rosenthal.  Games of perfect information, predatory pricing and the chain-store paradox , 1981 .

[26]  Yossi Feinberg,et al.  Subjective reasoning - dynamic games , 2005, Games Econ. Behav..

[27]  Geir B. Asheim,et al.  On the epistemic foundation for backward induction , 2002, Math. Soc. Sci..

[28]  Robert Stalnaker,et al.  Belief revision in games: forward and backward induction 1 Thanks to the participants in the LOFT2 m , 1998 .

[29]  G. H. BRYAN.  Proceedings of the Fifth International Congress of Mathematicians , 1914, Nature.

[30]  Andrés Perea,et al.  Minimal belief revision leads to backward induction , 2008, Math. Soc. Sci..

[31]  John W. Carroll,et al.  The Backward Induction Argument , 2000 .

[32]  Thorsten Clausing,et al.  BELIEF REVISION IN GAMES OF PERFECT INFORMATION , 2004, Economics and Philosophy.

[33]  Graham Priest,et al.  The Logic of Backwards Inductions , 2000, Economics and Philosophy.

[34]  A. Rubinstein.  COMMENTS ON THE INTERPRETATION OF GAME THEORY , 1991 .