Title: Undecidable Statements in Game Theory
Abstract: The paper points towards formally undecidable statements in non-cooperative game theory. We present a general theory where rational players base their decisions solely on the provable implications of their assumptions. For a version of the centipede game, we show that it is undecidable whether a deviation from the backward induction path is possible under commonly assumed rationality or not. The approach retraces various impossibility results in the definition of rational behavior to the presence of undecidable statements. It is argued that the problem of undecidability can be avoided by assuming that each player has a private epistemic model of his opponents.
Keywords: Rationality, Logic, Undecidability, Game Theory, Language, Iterated Dominance
JEL-Classification-Number: C72, A12
Creation-Date: June 1997
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