The Incompleteness of Theories of Games |
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| Authors: | Tsuji Marcelo da Costa Newton C. A. Doria Francisco A. |
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| Affiliation: | (1) Reseach Group on Logic and Foundations, Institute for Advanced Studies, University of São Paulo, 05655-010 São Paulo SP, Brazil (E-mail: Email;(2) Department of Physics, Institute for the Exact Sciences (ICE), Federal University at Juiz de Fora, Brazil (E-mail: Email |
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| 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. |
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| Keywords: | Chaitin incompleteness noncooperative games Richardson's functor undecidability |
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