Decision makers in complex situations such as in business, politics or sciences are not aware of all relevant facts when making decisions. They face not just uncertainty about which facts obtain but may be also unable to conceive of all relevant facts. Consequently, large resources are devoted to explore unmapped terrain, figure out opportunities, conceive of novelties, and to provide for unanticipated events. Yet, in economics, decision theory and game theory, it is assumed that decision makers can conceive of all relevant facts. Indeed, Modica and Rustichini (1994) and Dekel, Lipman and Rustichini (1998) showed that it is impossible to model unawareness with standard state-space models that are widely used to analyze incomplete information. This limits substantially the application of economic theory, decision theory and game theory.
The project is aimed to overcome the unrealistic assumption of full awareness, to provide a foundation for game theory with unawareness, and to explore the implications of asymmetric unawareness in economics. Based on prior work by Heifetz, Meier and Schipper (2006), an unawareness belief structure is developed, which has standard properties of probabilistic beliefs but nevertheless allows for unawareness. Using unawareness belief structures, Bayesian games with unawareness are introduced, equilibrium is defined, and the existence and structure of equilibria is analyzed. Such games are not necessarily "common knowledge" since players may have asymmetric awareness of payoff-relevant events, actions or opponents. The project would prove a "No-Agreement-to-Disagree" Theorem. As an application to markets, it is shown that speculative trade is possible under unawareness. Yet, a "No-Trade" Theorem is proved according to which arbitrary small transaction costs rule out speculation under unawareness. The project also develops dynamic games with unawareness including learning of new concepts and making others strategically aware of issues during the play. Games with unawareness are applied to incomplete contracts, the design of institutions, multi-issue bargaining and strategic framing.
The broader impact of this project is to provide tractable tools to the social scientist for analyzing situations with unanticipated events. These tools should be applicable to more complex situations ranging from business and finance over politics up to explorative sciences. The project is a contribution to formal logic, computer science and artificial intelligence since it provides a multi-person semantic structure for reasoning about unawareness and beliefs. Moreover, the project yields also a clear categorization of knowledge, belief and awareness, which is relevant to cognitive sciences. Altogether the research is expected to provide a better understanding of decision making with unanticipated events.
