The incompleteness of theories of games

Journal of Philosophical Logic 27 (6):553-568 (1998)
Abstract
We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.
Keywords Chaitin  incompleteness  noncooperative games  Richardson's functor  undecidability
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