Galeazzi, Paolo and Lorini, Emiliano Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces. ISSN In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces.
A Yabloesque paradox in epistemic game theory — the University of Bath's research portal
As shown in many papers see Aumann and Brandenburger in Econometrica —, ; Baltag et al. The main result of this paper is a formal comparison between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic—doxastic logic for belief and knowledge.
Consider a centipede game. The backward induction rationale is that if we reached the final stage, the final player would defect, hence if we are in the second-to-last stage I should see that coming and defect before her, hence if we are in the third-to-last stage she will see that coming and defect before me, and so on.
Epistemic Game Theory
Imagine that, however, player 1 does not defect in the first stage. What am I to infer? Was this a mistake or am I perhaps facing an irrational opponent? Backward induction requires that I never make such an inference, and hence I defect in stage 2.
Epistemic Game Theory: Complete Information
Here is a better justification for defection in the centipede game, though. That is, if it is possible for him to have some belief about my actions in the second stage which rationally justified his first stage action, then I must believe that he holds those beliefs. For example, he may believe that I believe he will continue again in the third stage, hence that I will continue in the second stage, hence he will continue in the first stage then plan to defect in the third stage. Given his beliefs about me, his actions in the first stage were rational.
But if that plan to defect in stage three were his justification, then I should defect in stage two.
He realizes I will make these inferences, hence he will defect in stage 1. That is, the backward induction outcome is justified by forward induction. But the epistemic justification is completely based on the equivalence between forward and backward induction under those assumptions, not on any epistemic justification for backward induction reasoning per se.
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