A theory of higher order probabilities
Proceedings of the 1986 Conference on Theoretical aspects of reasoning about knowledge
Operational Pointer Semantics: Solution to Self-Referential Puzzles I
Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge
Reasoning about Belief and Knowledge with Self-Reference and Time
Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge
Common Knowledge and Backward Induction: A Solution to the Paradox
Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge
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The "chain-store paradox" of Reinhard Selten is one of a number of scenarios involving the finite repetition of a certain kind of sub-game about which a paradoxical conclusion can be derived. In each of these cases, a backward-induction argument is used to prove that it is futile to try to establish a reputation for cooperative or punitive behavior through appropriate action in the early stages of the game, despite the fact that nearly all agree that it is intuitively reasonable to do so. Selten believed that this is paradoxical in the weak sense: a surprising, unexpected result of game theory. In this paper, I argue that it is paradoxical in the strong sense: a logical antinomy of rational belief or subjective probability, analogous to the paradox of the Liar.