NAAMSI · Non-Additive Axiomatic Models of Strategic Interaction

The aim of this project is twofold: (1) to provide an in-depth logical and axiomatic study of notions of expected utility based on non-additive measures of uncertainty, and (2) to apply this study to the investigation of alternative theories of non-cooperative games.Probability Theory is the most common model in the formalization of approximate reasoning in Computer Science and Artificial Intelligence, and offers the formal basis for a theory of decision and games through the concept of expected utility. However, many situations in which inference under uncertainty is required cannot be properly formalized within the probabilistic framework. For this reason, other measures of uncertainty have been introduced, the most notable ones being non-additive measures such as imprecise probabilities, belief functions, and possibility and necessity measures.The first part of this research aims at introducing many-valued logical systems to axiomatize, represent and reason about notions of expected utility based on non-additive uncertainty measures. This novel approach will allow to encode measure-theoretic and computational properties of non-probabilistic theories of decision in a purely logical framework.The second part aims at investigating the fundamental notions of a theory of games based on the above characterizations of non-probabilistic notions of expected utility. The goal is to define the basic concepts and investigate the main mathematical properties of n-person non-cooperative games with complete and incomplete information, relying on forms of expected utility based on non-additive plausibility measures.This research aims at developing cutting-edge investigation in the formalization of reasoning and decisions with uncertain information, by using uncertainty models alternative to probability theory. This will provide new foundations to theories of decision and strategic interaction that will have significant impact on other fields of research.""