A Non-Self-Referential Paradox in Epistemic Game Theory

TL;DR

This paper introduces a paradox in epistemic game theory demonstrating the impossibility of fully modeling players' beliefs and assumptions, supported by a new formal logic that highlights the limitations of such models.

Contribution

It presents a novel non-self-referential paradox and develops an interactive temporal assumption logic to formalize and analyze this paradox.

Findings

Complete epistemic belief models are impossible.

The new logic formalizes the paradox effectively.

No comprehensive interactive temporal assumption model exists.

Abstract

In game theory, the notion of a player's beliefs about the game players' beliefs about other players' beliefs arises naturally. In this paper, we present a non-self-referential paradox in epistemic game theory which shows that completely modeling players' epistemic beliefs and assumptions is impossible. Furthermore, we introduce an interactive temporal assumption logic to give an appropriate formalization of the new paradox. Formalizing the new paradox in this logic shows that there is no complete interactive temporal assumption model.