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CRETA Seminars in Economic Theory

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CRETA Seminar - Martin Meier (Bath)

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Location: S2.79

This is part of the CRETA Seminar Series, Seminar organisers: Sinem Hidir and Costas Cavounidis.

Abstract of the talk: Perfect Quasi-Perfect Rationalizability (Martin Meier and Andres Perea)

In this paper, we consider backward-induction reasoning in dynamic games, where players only reason about the future, but not the past. Moreover, we assume that players believe that they may make mistakes themselves in the future.

So far, there is no rationalizability concept that allows for this possibility.
Here, we define a rationazability analog of trembling hand perfect equilibrium (THPE) (Selten 1975), which we call trembling hand perfect rationalizability (THPR).
In THPE, as well as in THPR, a player might attribute himself higher mistake probabilities than to others. We consider this as unnatural and overcome this problem by imposing that a player deems his own mistakes infinitely less likely than the combined mistakes of his opponents.
This leads to a concept that we call perfect quasi-perfect rationalizability (PQPR), which by definition, is a refinement of THPR. Blume and Meier (2017) propse, based on the same idea, the concept of perfect quasi-perfect equilibrium, the euqilibrium analog of PQPR.

Asheim and Perea 2005 defined a rationalizability analog of quasi-perfect Equilibrium (QPE), called quasi-perfect rationalizabilibty (QPR). We prove that PQPR is a refinement of QPR.
We also show that PQPR strategies always exist for every player in every finite extensive form game with perfect recall.

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