A Plausibility Model for Regret Games
In this paper we develop a plausibility model by defining a new notion of rationality based on the assumption that a player believes that she doesn’t play a regret dominated strategy. Especially, we show that the interactive epistemic outcomes of this type of rationality are in line with the solutions of the Iterated Regret Minimization (IRM) algorithm. So, we state that one can achieve a characterization of the IRM algorithm by keeping upgrading the assumption of rationality, and we obtain common belief of rationality in the limit model. A benefit of our characterization is that it provides the epistemic foundation to the IRM algorithm and solve a dynamic information problem best expressed through the Traveler’s Dilemma. Meanwhile, we also link solutions of the IRM algorithm to modal \(\mu \)-calculus to deepen our understanding of the epistemic characterization.
KeywordsRegret games Iterated regret minimization algorithm Plausibility model \(\mu \)-calculus Modal logic Traveler’s Dilemma Information dynamics
For this work the first author benefited financial support from the University of Pisa, the paper is also supported by Kep Programm of National Social Science Foundation of China (No. 16AZX017) and by Kep Programm of National Social Science Foundation of China (No. 15AZX020). The authors would like to thank Alexandru Baltag, Alessandro Berarducci, Davide Grossi and Johan van Benthem for their precious suggestions and comments.
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