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Descriptive complexity and revealed preference theory

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  • Galambos, Adam

Abstract

This paper formalizes revealed preference theory using the notion of Ramsey eliminability in logic, and shows how the language required to state a revealed preference axiom for some choice theory is closely connected with the computational tractability of testing that theory. The connection is made through results in descriptive complexity theory, a relatively new field in finite model theory. It is shown that checking whether observed choices of players in normal form games are Nash rationalizable is an NP-complete problem. This also means that there does not exist an analogue (in a precise sense) of the Strong Axiom of Revealed Preference for Nash equilibrium.

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  • Galambos, Adam, 2019. "Descriptive complexity and revealed preference theory," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 54-64.
    • Handle: RePEc:eee:matsoc:v:101:y:2019:i:c:p:54-64
    DOI: 10.1016/j.mathsocsci.2019.06.006
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    References listed on IDEAS

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    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    3. Backhouse, Roger E., 2017. "Founder of Modern Economics: Paul A. Samuelson: Volume 1: Becoming Samuelson, 1915-1948," OUP Catalogue, Oxford University Press, number 9780190664091.
    4. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
    5. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April.
    6. Hands,D. Wade, 2001. "Reflection without Rules," Cambridge Books, Cambridge University Press, number 9780521797962.
    7. Gradwohl, Ronen & Shmaya, Eran, 2015. "Tractable Falsifiability," Economics and Philosophy, Cambridge University Press, vol. 31(2), pages 259-274, July.
    8. Chambers, Christopher P. & Echenique, Federico & Shmaya, Eran, 2017. "General revealed preference theory," Theoretical Economics, Econometric Society, vol. 12(2), May.
    9. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
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