Forward induction reasoning revisited

Battigalli and Siniscalchi (2002) formalize the idea of forward induction reasoning as "rationality and common strong belief of rationality" (RCSBR). Here, we study the behavioral implications of RCSBR across all type structures. Formally, we show that RCSBR is characterized by a solution concept we call Extensive Form Best Response Sets (EFBRS's). It turns out that the EFBRS concept is equivalent to a concept already proposed in the literature, namely Directed Rationalizability. (See Battigalli and Siniscalchi 2003.) We conclude by applying the EFBRS concept to games of interest.

[1]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

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

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

[4]  Pierpaolo Battigalli,et al.  Rationalization and Incomplete Information , 2003 .

[5]  Elchanan Ben-Porath,et al.  Signaling future actions and the potential for sacrifice , 1992 .

[6]  D. Fudenberg,et al.  Perfect Bayesian equilibrium and sequential equilibrium , 1991 .

[7]  H. Jerome Keisler,et al.  Admissibility in Games1 , 2008 .

[8]  Pierpaolo Battigalli,et al.  Strategic Independence and Perfect Bayesian Equilibria , 1996 .

[9]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[10]  Pierpaolo Battigalli,et al.  Interactive epistemology in games with payoff uncertainty , 2007 .

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

[12]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[13]  Pierpaolo Battigalli,et al.  Context-Dependent Forward Induction Reasoning , 2009 .

[14]  Pierpaolo Battigalli,et al.  Rationalizability in Incomplete Information Games , 1999 .

[15]  Pierpaolo Battigalli,et al.  Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information , 2013 .

[16]  Pierpaolo Battigalli,et al.  Interactive beliefs, epistemic independence and strong rationalizability , 1999 .

[17]  Leslie M. Marx,et al.  Order Independence for Iterated Weak Dominance , 2000, Games Econ. Behav..

[18]  Marciano M. Siniscalchi,et al.  Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games , 1999 .

[19]  Adam Brandenburger,et al.  Self-admissible sets , 2010, J. Econ. Theory.

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

[21]  A. Kechris.  Classical descriptive set theory , 1987 .

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

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

[24]  A. Rényi.  On a new axiomatic theory of probability , 1955 .

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

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