Meinhardt, Holger Ingmar (2015): The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself.
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Abstract
Recently, we had to realize that more and more game theoretical articles have been published in peer-reviewed journals with severe logical deficiencies. In particular, we observed that the indirect proof was not applied correctly. These authors confuse between statements of propositional logic. They apply an indirect proof while assuming a prerequisite in order to get a contradiction. For instance, to find out that ``if A then B'' is valid, they suppose that the assumptions ``A and not B'' are valid to derive a contradiction in order to deduce ``if A then B''. Hence, they want to establish the equivalent proposition ``A and not B implies A and not A'' to conclude that ``if A then B''is valid. In fact, they prove that a truth implies a falsehood, which is a wrong statement. As a consequence, ``if A then B'' is invalid, disproving their own results. We present and discuss some selected cases from the literature with severe logical flaws, invalidating the articles.
Item Type: | MPRA Paper |
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Original Title: | The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself |
Language: | English |
Keywords: | Transferable Utility Game; Solution Concepts; Axiomatization; Propositional Logic, Material Implication; Circular Reasoning (circulus in probando); Indirect Proof; Proof by Contradiction; Proof by Contraposition; Cooperative Oligopoly Games |
Subjects: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games |
Item ID: | 75876 |
Depositing User: | Dr. Holger Ingmar Meinhardt |
Date Deposited: | 29 Dec 2016 09:20 |
Last Modified: | 10 Dec 2024 10:11 |
References: | J. Kleppe, J. H. Reijnierse, and P. Sudhölter. Axiomatizations of Symmetrically Weighted Solutions. Annals of Operations Research, pages 1–17, 2013. ISSN 0254-5330. doi: 10.1007/s10479-013-1494-1. URL http://dx.doi.org/10.1007/s10479-013-1494-1. A. Lardon. The gamma-core in Cournot oligopoly TU-games with capacity constraints. Theory and Decision, 72(3):387–411, 2012. ISSN 0040-5833. doi: 10.1007/s11238-011-9256-5. URL http://dx.doi.org/10.1007/s11238-011-9256-5. H. I. Meinhardt. Finding the nucleoli of large cooperative games: A disproof with counter-example. CoRR, abs/1603.00226, 2016. URL http://arxiv.org/abs/1603.00226. N.Watanabe and S. Muto. Stable Profit Sharing in a Patent Licensing Game: General Bargainng Outcomes. International Journal of Game Theory, 37(4):505–523, 2008. ISSN 0020-7276. doi: 10.1007/s00182-008-0130-9. URL http://dx.doi.org/10.1007/s00182-008-0130-9. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/75876 |
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The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself. (deposited 16 Sep 2015 04:25)
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