Regular ArticleA Note on the Implications of Common Knowledge of Rationality
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The existence of universal qualitative belief spaces
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2023, Economics LettersLearning to agree over large state spaces
2022, Journal of Mathematical EconomicsCitation Excerpt :An analogous question has been studied in game-theoretical contexts. Specifically, Lipman (1994) shows that in some games it is possible to attain common knowledge of rationality only through a transfinite process of elimination of never-best replies. Finally, we do not claim that transfinite dialogues are necessary in every possible situation covered by our model.
Common belief in rationality in psychological games: Belief-dependent utility and the limits of strategic reasoning
2022, Journal of Mathematical EconomicsCitation Excerpt :Theorem 4.3, Example 4.1, and Theorem 5.5 show a striking similarity between strategic reasoning in psychological games and strategic reasoning in traditional games with infinite choice and/or player sets: Firstly, in both classes of games, it is not guaranteed that common belief in rationality can be satisfied, even if arbitrary finite orders of belief in rationality are satisfiable (see Dufwenberg and Stegeman, 2002, Example 2). Secondly, selecting the choices consistent with common belief in rationality might necessitate an elimination procedure of arbitrary transfinite length, rather than a countably infinite one (see Lipman, 1994). A notable implication of these remarks is that the gap between finite psychological games as in Definition 2.1 and psychological games with infinite choice- and player-sets becomes very small:
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