Epistemic characterizations of iterated deletion of inferior strategy profiles in preference-based type spaces

Abstract

Bonanno (Logics and the foundations of game and decision theory, Amsterdam University Press, Amsterdam, 2008) provides an epistemic characterization for the solution concept of iterated deletion of inferior strategy profiles (IDIP) by embedding strategic-form games with ordinal payoffs in non-probabilistic epistemic models which are built on Kripke frames. In this paper, we will follow the event-based approach to epistemic game theory and supplement strategic games with type space models, where each type is associated with a preference relation on the state space. In such a framework, IDIP can be characterized by the conditions that at least one player has correct beliefs about the state of the world and that there is common belief that every player is rational, has correct beliefs about the state of the world and has strictly monotone preferences. Moreover, we shall compare the epistemic motivations for IDIP and its mixed strategy variant known as strong rationalizability (SR). Presuppose the above conditions. Whenever there is also common belief that players’ preferences are representable by some expected utility function IDIP still applies. But if there is common belief that players’ preferences are representable by some expected payoff function, then SR results.