The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself

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.