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 peerreviewed 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 

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:  08 Jul 2020 20:58 
References:  J. Kleppe, J. H. Reijnierse, and P. Sudhölter. Axiomatizations of Symmetrically Weighted Solutions. Annals of Operations Research, pages 1–17, 2013. ISSN 02545330. doi: 10.1007/s1047901314941. URL http://dx.doi.org/10.1007/s1047901314941. A. Lardon. The gammacore in Cournot oligopoly TUgames with capacity constraints. Theory and Decision, 72(3):387–411, 2012. ISSN 00405833. doi: 10.1007/s1123801192565. URL http://dx.doi.org/10.1007/s1123801192565. H. I. Meinhardt. Finding the nucleoli of large cooperative games: A disproof with counterexample. 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 00207276. doi: 10.1007/s0018200801309. URL http://dx.doi.org/10.1007/s0018200801309. 
URI:  https://mpra.ub.unimuenchen.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)
 The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself. (deposited 29 Dec 2016 09:20) [Currently Displayed]