The purpose of this study is to investigate the value-relevance of corporate sustainability disclosure through integrated reporting. Sustainability disclosure is subject to managers’ discretion. Besides, it is often hardly verifiable. In this respect, integrated reporting could provide the means for a verifiable disclosure, otherwise, in the jargon of game theory, it could be considered as a cheap talk. This paper investigates which of these hypotheses is most likely to occur in reality. In order to do this, a simple theoretical framework is introduced, where sustainability of corporate performances is modelled as a tail-risk for shareholders. Costless signaling games (cheap talk) and persuasion games are reviewed within this context, in order to derive competing theories of sustainability disclosure’s value relevance through integrated reporting. These alternative theories are tested empirically consistent with the theoretical framework presented, in order to identify key-parameters. In this respect, a systematic textual analysis (artificial intelligence) of integrated reports was employed as to build a synthetic measure of sustainability disclosure. The application of this methodology on a sample of European listed companies showed that sustainability disclosure through integrated reporting has no effect on market-valuations, confirming the null hypothesis of integrated reporting resulting in a cheap talk’s babbling equilibrium.