Date: Tuesday, October 15th
Presenter: Niels Mourmans
Authors: Niels Mourmans (KE, UM)
Title: When is iterated elimination of choices enough in psychological games?
Abstract: The framework of psychological game theory has allowed for the modelling of a wide range of belief-dependent motivations. At the same time, analysing psychological games can get complex rather quickly due to the fact that higher- order beliefs may enter the utility functions. As a result, some nice properties of traditional games fail to carry over to psychological games in general. This includes the failure of the iterated elimination of strictly dominated choices (IESDC) to always exactly characterize the choices that are rationally played under belief hierarchies expressing common belief in rationality (CBR). In this paper we characterize the families of two-player expectation-based psychological games for which IESDC yields exactly the choices that are rationally played under CBR. We characterize these games based on which orders of beliefs are directly utility-relevant for a decision-maker. We identify three cases. Two of these are relatively trivial: (i) the decision-maker’s utility depends on a single, even order of belief and (ii) the decision-maker’s utility and her opponent’s utility depend on a single order of belief. We also identify a third, non-trivial case. Our novel notion of causality diagrams, which capture those orders of beliefs that are (indirectly) utility-relevant, is used to obtain our results.