Giacomo Bonanno and Elias Tsakas, Qualitative analysis of common belief of rationality in strategic-form games.
study common belief of rationality in strategic-form games with ordinal
utilities, employing a model of qualitative beliefs. We characterize
the three main solution concepts for such games, viz., Iterated
Deletion of Strictly Dominated Strategies (IDSDS), Iterated Deletion of
Boergers-dominated Strategies (IDBS) and Iterated Deletion of Inferior
Strategy Profiles (IDIP), by means of gradually restrictive properties
imposed on the models of qualitative beliefs. As a corollary, we prove
that IDIP refines IDBS, which refines IDSDS.
Giacomo Bonanno, Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction.
Doxastic characterizations of the set of Nash equilibrium outcomes and of the set of backward-induction outcomes are provided for general perfect-information games (where there may be multiple backward-induction solutions). We use static models that are behavioral, rather than strategy-based, where a state only specifies the actual play of the game and not the hypothetical choices of the players at nodes that are not reached by the actual play. The analysis is completely free of counterfactuals and no belief revision theory is required, since only the beliefs at reached histories are specified..
To download the files in pdf format click here: Lecture 1.pdf , Lecture 2.pdf
Giacomo Bonanno (with Klaus Nehring), Agreeing to disagree: a survey.
To download the paper in pdf format click here: agree.pdf
Some of the material in this paper was published in: Giacomo Bonanno
and Klaus Nehring, “How to make sense of the common prior assumption under
incomplete information", International Journal
of Game Theory, 28 (3), August 1999, pp. 409-434 (To download the paper
in pdf format click here: common.pdf)